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Henri Poincaré

1854-1912 · mathematics, theoretical physics, astronomy, philosophy of science
French mathematician, theoretical physicist, and philosopher of science. He laid the foundations of special relativity, predicted the existence of gravitational waves, and made fundamental contributions to celestial mechanics, topology, and chaos theory. He is considered one of the greatest mathematicians of all time and the last universalist capable of covering all science.

Biography

Born in Nancy, France. Studied at the École Polytechnique and the École des Mines in Paris. He was a professor at the Sorbonne and a member of the French Academy of Sciences. In addition to physics and mathematics, he engaged in the philosophy of science and wrote several well-known books on methodology. His cousin was the President of France, Raymond Poincaré. He received many awards, including the Lorentz Medal.

Key discoveries

💡 Poincaré had a phenomenal memory and the ability to visualize multidimensional spaces; he solved complex problems mentally without using drafts. Despite severe nearsightedness, he never wore glasses, preferring his inner world.
"He considered science a cemetery of hypotheses where many beautiful ideas rest."
Concepts
differential formgravitational wavesspeed of light
Laws
principle of constancy of the speed of lightLorentz transformationsprinciple of least actionPoincaré recurrence theorem
Scientists
Fritz ZwickyRainer WeissStephen HawkingJames Clerk MaxwellJoseph WeberHendrik LorentzChristian DopplerArthur Compton

Related articles

physics.data-an2008-05-222 minarXiv:0805.3464
Hidden Rhythms of El Niño: What Daily Data Reveal
A barometer on the island of Tahiti and a barometer in the Australian city of Darwin show different pressures. Subtract one from the other, and you get a number that climatologists call the Southern Oscillation Index. It changes every day, but within these daily jumps hide steady rhythms, just as the beats of a metronome hide within the noise of an orchestra.
Filippo Petroni·Marcel Ausloos
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Atmospheric and Oceanic Physics2008-12-283 minarXiv:0812.4846
Climate seesaws that get stuck
A seesaw with two children rarely balances perfectly. It tips either left or right, pausing at the extremes for a moment before swinging back. The tropical Pacific behaves similarly: it either warms up off the coast of Peru (El Niño) or cools down (La Niña), and these states can last for months, sometimes over a year.
Tian Ma·Shouhong Wang
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Math Physics2009-03-122 minarXiv:0903.2106
An Air Pendulum Over the Pacific
In the 1920s, British meteorologist Gilbert Walker, trying to forecast monsoons in India, noticed a strange connection: when air pressure rises over the eastern Pacific, it falls over the western Pacific, and vice versa. It was as if a giant air pendulum were swinging along the equator.
Tian Ma·Shouhong Wang
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Atmospheric and Oceanic Physics2010-02-042 minarXiv:1002.1024
The Swing That Ignores the Push: Why the Annual Rhythm Produces a Three-Year Cycle
A swing builds up when you push it in time. But sometimes the person on the swing responds not to every push but to every third one, and the amplitude grows slowly yet inexorably.
A. Bershadskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillator
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Atmospheric and Oceanic Physics2010-02-262 minarXiv:1003.0028
El Niño's Seasonal Pulse: How Delayed Ocean Waves Lock the Phase
The ocean is like a pendulum with a memory. A push from seasonal winds returns not immediately but months later, when a wave crosses the Pacific. This delay, the authors argue, is what makes El Niño and La Niña repeatedly peak at the same time of year.
Ilya Zaliapin·Michael Ghil
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Dynamical Systems2011-09-132 minarXiv:1109.2818
Climate as a Road Map: Bifurcations and Resonances of El Niño
The Pacific Ocean does not breathe evenly but in bursts. Every few years, its warm waters stir, and then Australia suffocates from drought while Peru is flooded with rain. This phenomenon is called El Niño, and it resembles a traveler wandering along an invisible road map.
Bernd Krauskopf·Jan Sieber
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Popular Physics2011-11-112 minarXiv:1111.2845
Depth as a Measure of Natural Complexity
A team assembling a jigsaw puzzle from random pieces: how many simultaneous moves does it take to complete the picture? If the pieces are independent, they all go down at once. If each piece depends on the previous one, you have to work one at a time. So it is with systems: some states assemble instantly, others require a long sequential effort.
Jon Machta
Henri PoincaréEmmy NoetherJohn von Neumannuniform convergenceoptimization
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Chaotic Dynamics2012-01-233 minarXiv:1201.4679
One-Third Resonance: Why Climate and the Sun Swing in Sync
A swing pushed once per second usually oscillates once per second. But if you push it harder and at the right rhythm, it can swing three times slower: one full swing for every three pushes. Physicists call this subharmonic resonance, and it seems to govern the most prominent climate and solar oscillations.
A. Bershadskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillator
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Atmospheric and Oceanic Physics2012-06-252 minarXiv:1206.5657
El Niño: Chaos or Noise?
The ocean is like a drum beaten by the random hammer of the atmosphere. El Niño is a warm patch in the tropical Pacific that arrives every few years and alters weather across the globe. Scientists have long debated whether El Niño works like a precise clockwork that can be predicted, or like a roll of the dice where each throw is independent of the last.
Tatjana Zivkovic·Kristoffer Rypdal
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2012-06-252 minarXiv:1206.5828
El Niño as Conductor: How Climate Ties Together Earth's Rotation and Carbon Dioxide
A vast tongue of warm water rises to the surface of the tropical Pacific, and the entire climate system begins to resonate in unison. This is El Niño, the most powerful natural climate oscillation, affecting weather from Australia to Alaska.
A. Mazzarella·A. Giuliacci·N. Scafetta
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Atmospheric and Oceanic Physics2014-11-042 minarXiv:1411.0815
Ocean Sloshing as a Clock: An El Niño Model via the Mathieu Equation
In 1981, the ocean off the coast of Peru behaved strangely. The warm current that usually arrives every few years changed its rhythm, and scientists still argue about what exactly shifted. A new study offers a simple answer: the ocean sloshes like water in a bowl that is rocked by tides and Earth's rotation.
Paul R. Pukite
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Dynamical Systems2014-11-182 minarXiv:1411.5069
Forecasting Without a Model: Nonparametric Prediction of Chaos and Climate
A translator learns not from a dictionary but from speech. They listen to native speakers and pick up rules that are written in no textbook. Similarly, a new method for forecasting complex systems such as climate or turbulence does not require knowing their equations. Instead, it looks at data and learns to predict their behavior.
Tyrus Berry·Dimitrios Giannakis·John Harlim
Henri PoincaréPeter ShorIsaac NewtonDiffusion Modelschaos theoryStochastic modelingstochastic processesdifferential equation
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Atmospheric and Oceanic Physics2015-01-262 minarXiv:1501.06265
The Coast as Rain Conductor
The coast works like a conductor: it doesn't create the music, but it sets the rhythm and direction. Every morning, the sun heats the land faster than the sea, and warm air rises over the sand, pulling in a moist breeze from the ocean. By evening, the land cools and the wind reverses. This daily pendulum lines up clouds along the water's edge, like musicians following the baton.
Martin Bergemann·Christian Jakob·Todd P. Lane
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemscontrol theoryprobability theory
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Dynamical Systems2015-06-022 minarXiv:1506.00756
Rhythm Thrown Off by Wind: How Noise Blurs Oscillations
A pendulum swings steadily until gusts of wind disturb it. Each push shifts the rhythm slightly, and soon the beats no longer match the metronome. Natural oscillators live the same way: the heart, populations, climate cycles—they all oscillate, but randomness constantly interferes.
Stilianos Louca
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemsharmonic oscillatornonlinear dynamicschaos theory
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Geophysics2015-06-123 minarXiv:1506.04066
A Map That Could Have Predicted El Niño
In 1997, the Pacific Ocean off the coast of Peru warmed so much that fish disappeared and torrential rains hit the desert. This is El Niño, a warm current that every few years changes weather across the planet. Predicting its arrival six months ahead is already possible, but looking further is like guessing a ship's route from a single point on a map.
H. F. Astudillo·R. Abarca-del-Rio·F. A. Borotto
Henri Poincaréchaos theory
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Applied Statistics2015-07-122 minarXiv:1507.03283
How to Predict Heat a Year in Advance
On April 16, 2012, Washington experienced heat no one expected. The thermometer climbed 18 degrees above normal. Sixty days earlier, Bucharest and Kyiv had weather unusual for them. The link between these events was found by an algorithm that scans pairs of cities worldwide, looking for recurring coincidences.
Dmytro Zubov·Humberto A. Barbosa·Gregory S. Duane
Henri Poincaréchaos theory
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Dynamical Systems2015-11-233 minarXiv:1511.07472
The Pacific Pendulum: Why El Niño Erupts Once a Decade
The Pacific pendulum swings irregularly. Sometimes it barely trembles near the bottom, and sometimes it suddenly makes a giant sweep that disrupts weather across the planet. El Niño, the warm current in the equatorial Pacific, recurs every few years, but truly strong events happen once every 10–20 years, and until now no one could explain why they appear so irregularly.
Andrew Roberts·Esther Widiasih·Axel Timmermann·Christopher K. R. T. Jones·John Guckenheimer
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Geophysics2016-04-063 minarXiv:1604.01742
The Ocean Conducts Its Own Orchestra: How Nonlinear Analysis Reveals Hidden Rhythms of the Indo-Pacific
An orchestra without a conductor: the instruments set their own rhythm. That is how one might describe the climate system of the Indo-Pacific region, where sea surface temperatures oscillate across many time scales, from seasonal to multi-decadal. Previously, to hear a single instrument, you had to pre-tune filters, cutting off everything else.
Joanna Slawinska·Dimitrios Giannakis
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Statistical ML2016-05-302 minarXiv:1605.09370
El Niño Without a Teacher: How an Algorithm Heard Climate in Ocean Noise
A translator sits in a hall where people speak an unfamiliar language. They don't understand the words, but they hear how the tone shifts: sometimes calm and steady, sometimes excited and sharp. From intonation alone, they guess what is being discussed.
Krzysztof Chalupka·Tobias Bischoff·Pietro Perona·Frederick Eberhardt
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2016-07-092 minarXiv:1607.02645
The Pacific Ocean Pendulum: Why Strong El Niños Are Unpredictable
In 2014, forecasters around the world were expecting a powerful El Niño. The ocean had warmed, the trade winds had weakened, all the signs were there. But the event only came a year later. The Pacific seemed to change its mind.
John Guckenheimer·Andrew Roberts·Axel Timmermann·Henk Dijkstra
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2016-09-023 minarXiv:1609.00547
Climate Network: How El Niño Tightens Its Grip and Strikes with Precision
A warm tongue of water stretches along the equatorial Pacific, and within weeks, Peru sees torrential rains while Australia's pastures dry out. That is how El Niño begins: a natural conductor that, at critical moments, makes only a few orchestra members play, but much louder.
Jingfang Fan·Jun Meng·Yosef Ashkenazy·Shlomo Havlin
Henri PoincaréJohn von NeumannIsaac Newtonnonlinear dynamics
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Atmospheric and Oceanic Physics2016-09-293 minarXiv:1609.09185
An Orchestra Without a Conductor: How the Ocean and Atmosphere Strike a Deal
In 1972, anchovies vanished off the coast of Peru. Fishermen were left empty-handed, and the world learned the word El Niño. Since then, scientists have been searching for ways to predict when that warm current will once again upend the planet's weather.
Dimitrios Giannakis·Joanna Slawinska
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Geophysics2016-11-242 minarXiv:1611.09167
The River That Refuses to Speed Up
The Paglia River behaves like a pendulum that resists being pushed. If a sudden influx of water pours in, the river does not keep gaining strength but quickly swings back to its usual level. This behavior is called antipersistence, and it was found in a twenty-two-year record of half-hourly discharge measurements near the Italian town of Orvieto.
Marcel Ausloos·Roy Cerqueti·Claudio Lupi
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Atmospheric and Oceanic Physics2017-03-202 minarXiv:1703.06662
Seasonal Forecasts for China's Energy Sector: Where the System Really Works
Picture a map of China with sparse green patches scattered across a yellow desert. Those patches are where the GloSea5 climate model can genuinely look three months ahead, while the desert is everything else, where its forecasts are no better than a coin toss.
Philip E. Bett·Hazel E. Thornton·Julia F. Lockwood·Adam A. Scaife·Nicola Golding·Chris Hewitt·Rong Zhu·Peiqun Zhang·Chaofan Li
Henri Poincaréchaos theory
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Geophysics2017-03-272 minarXiv:1703.09138
El Niño: Predicting Strength and Onset a Year in Advance
An orchestra falls out of tune before a storm, then plays in unison again. In the equatorial Pacific, within a rectangle stretching from 5°S to 5°N and from 120°W to 170°W, water temperatures usually change in concert, like musicians playing the same part. This area is called the Niño 3.4 region.
Jun Meng·Jingfang Fan·Yosef Ashkenazy·Armin Bunde·Shlomo Havlin
Henri Poincaréchaos theory
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Fluid Dynamics2017-05-173 minarXiv:1705.06207
An Orchestra Without a Conductor: Slow Rossby Waves Set the Climate's Rhythm
Over the tropical Pacific, air pressure breathes with periods from two to fourteen years. The barometer on Tahiti rises while it falls in Darwin, Australia, and the entire planet's climate shudders: El Niño arrives. Meteorologists call this the Southern Oscillation and have tracked it for 138 years, but until now they couldn't answer a simple question: where do such periods come from?
T. Elperin·N. Kleeorin·I. Rogachevskii
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Atmospheric and Oceanic Physics2017-05-232 minarXiv:1705.08171
Two Pacific Ocean Pendulums: How Linked Regions Give Birth to and Quench El Niño
Two pendulums hang side by side, connected by a spring. Give one a push, and through the spring the other starts to swing. That's how the two regions of the equatorial Pacific are arranged, where sea-surface temperature rises and falls in the rhythm of El Niño.
Chandrakala Meena·Shweta Kumari·Akansha Sharma·Sudeshna Sinha
Henri Poincaréchaos theory
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Stellar2017-06-282 minarXiv:1706.09105
The Sun's Two Pendulums: How Coupled Oscillations Create a 90-Year Rhythm
Place two pendulums side by side and give one a gentle push; the other will soon pick up the rhythm. This behavior isn't limited to clocks on a shared shelf; it also applies to the plasma inside the Sun. In the star's convection zone, two huge ring-shaped flows circulate: one closer to the surface, the other deeper. Each oscillates with its own period—12.05 and 9.52 years.
Yasushi Muraki
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemssolar cycle
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Chaotic Dynamics2017-07-282 minarXiv:1707.09853
Two Ocean Pendulums Sing in Unison
Two pendulums hang from the same wall, with a spring stretched between them. Each on its own can swing or stay still, but connect them and a shared dance begins: one nudges the other, and oscillations spread through the whole setup. That's how the Pacific Ocean works, where two neighboring regions exchange heat through waves.
Chandrakala Meena·Elena Surovyatkina·Sudeshna Sinha
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systemschaos theory
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Atmospheric and Oceanic Physics2017-09-083 minarXiv:1709.02606
A Trail in the Sand: How 135 Years of Weather Yielded the El Niño Equation
A trail in the sand stretches across the entire beach. The animal passed here at night, and from its footprints you can reconstruct not only its size but also its gait: where it sped up, where it slowed down, how it shifted its weight. That is essentially what researchers did with El Niño.
Shivsai Ajit Dixit·B N Goswami
Henri PoincaréJohn von NeumannIsaac Newtonnonlinear dynamics
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physics.gen-ph2017-09-212 minarXiv:1709.07146
An Ocean Thermometer Instead of a Barometer: A New Take on Climate Indices
For a century, climatologists have measured the ocean's pulse with a barometer. Indices like El Niño or the North Atlantic Oscillation are built on atmospheric pressure differences between two points, and then we wonder why rivers don't obey.
Jishi Zhang·Jingrong Lu·Haidong Huang·Xiaoning Liu·Yafeng Zhao·Zhiyang Wang·Jinlei Mo
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Dynamical Systems2017-10-092 minarXiv:1710.03216
The Pendulum That Forgets How to Swing
In 2014, forecasters expected a strong El Niño, but it arrived only a year later. The ocean seemed to change its mind. Researchers studied a simple model of the tropical Pacific and found that the system has two distinct "personalities": one regularly generates powerful El Niños, while the other oscillates chaotically without them. This model resembles a pendulum that sometimes jumps to a different swing.
John Guckenheimer·Axel Timmermann·Henk Dijkstra·Andrew Roberts
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2018-01-033 minarXiv:1801.00891
Relay of Chaos: How Warm Pacific Waters Make Weather Unpredictable
In the 1960s, meteorologist Edward Lorenz discovered that the air above our planet behaves like a crowd at a sale: the slightest nudge can change everything. His famous question about a butterfly in Brazil causing a tornado in Texas became a symbol of chaos in the atmosphere. But Lorenz only looked at the air. He left the ocean, which covers seven-tenths of the globe, out of the picture.
Marat Akhmet·Mehmet Onur Fen·Ejaily Milad Alejaily
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2018-03-232 minarXiv:1803.08909
El Niño and the Indian Monsoon: A Connection Under Pressure
The dance between two partners, the ocean and the sky, has been going on for thousands of years. El Niño warms the Pacific, and usually at the same time seasonal rains over India weaken. But in recent decades, the rhythm seems off: rains don't always respond to the warm current.
Mátyás Herein·Gábor Drótos·Tamás Bódai·Frank Lunkeit·Valerio Lucarini
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Applied Statistics2018-04-054 minarXiv:1804.01809
A Council of a Hundred Short Experts Predicts El Niño's Whims
The barometer in the port of Papeete on Tahiti and the one in Darwin, Australia, are separated by 7,400 kilometers. When one shows high pressure, the other often shows low, and this difference, called the Southern Oscillation, drives rainfall from India to Brazil. Predicting it even a month ahead is a problem with a century-long history.
Sean van der Merwe
Henri PoincaréJohn von NeumannIsaac Newtonnonlinear dynamics
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Atmospheric and Oceanic Physics2018-05-013 minarXiv:1805.00397
The Breath of Monsoons: How Random Gusts Settle into a Predictable Rhythm
Every summer, the same performance unfolds over the Indian Ocean: moist air rushes from the sea onto the scorched land, bringing rains that billions of people depend on.
A. Bershadskii
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2018-05-152 minarXiv:1805.05525
The Cold Dance Around Antarctica: A Wave That Never Stands Still
It takes eight years for a wave to circle Antarctica. It carries warmth and cold in turn, and sea ice advances and retreats with its crests. Previously, researchers caught this wave using different methods and saw either a propagating signal or a frozen dipole. Now it's clear: the dipole is just a snapshot of the wave when it stretches between two oceans.
Xinyang Wang·Dimitrios Giannakis·Joanna Slawinska
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Instrumentation2018-05-233 minarXiv:1805.09058
The Forest That Sometimes Falls Silent, Sometimes Sings: The Dynamics of the Drake Equation
The Galaxy is a forest where birds don't start singing right away. First, trees must grow — stars, around which planets eventually appear. The Drake equation counts how many birds might be singing in this forest right now, but it implicitly assumes that their number doesn't change: as many as there are, that's how many there have always been.
A. D. Panov
Emmy NoetherHenri PoincaréJohn von NeumannDynamical Systems
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Chaotic Dynamics2018-08-243 minarXiv:1808.08075
Ocean Memory Quenches El Niño Chaos
A warm current off the coast of South America shifts weather across the planet every few years. This is El Niño, and its behavior resembles a pendulum that sometimes swings too far. In 1986, meteorologist John Vallis described the process with three equations in which the ocean and atmosphere exchange heat and momentum.
Amey S. Deshpande·Varsha Daftardar-Gejji
Henri Poincaréchaos theory
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Atmospheric and Oceanic Physics2018-09-044 minarXiv:1809.00878
The Monsoon That Turned Out More Predictable Than We Thought
The Indian summer monsoon feeds a fifth of humanity, but its seasonal forecast has been considered nearly hopeless for decades: the potential predictability limit was estimated at only 45% of explained variability.
Subodh Kumar Saha·Anupam Hazra·Samir Pokhrel·Hemantkumar S. Chaudhari·K. Sujith·Archana Rai·Hasibur Rahaman·B. N. Goswami
Henri Poincaréchaos theory
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