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James Alan Yorke
Born	James Alan Yorke (1941-08-03) August 3, 1941 (age 83) Plainfield, New Jersey
Nationality	American
Alma mater	Columbia University (BA) University of Maryland, College Park (PhD)
Known for	Kaplan–Yorke conjecture
Awards	Japan Prize (2003)
Scientific career
Fields	Math and Physics (theoretical)
Institutions	University of Maryland, College Park
Doctoral students	Tien-Yien Li

James A. Yorke (born August 3, 1941) is a Distinguished University Research Professor of Mathematics and Physics and former chair of the Mathematics Department at the University of Maryland, College Park.

Life and career

Born in Plainfield, New Jersey, United States, Yorke attended The Pingry School, then located in Hillside, New Jersey. Yorke is now a Distinguished University Research Professor of Mathematics and Physics with the Institute for Physical Science and Technology at the University of Maryland. In June 2013, Yorke retired as chair of the University of Maryland's Math department. He devotes his university efforts to collaborative research in chaos theory and genomics.

He and Benoit Mandelbrot were the recipients of the 2003 Japan Prize in Science and Technology: Yorke was selected for his work in chaotic systems. In 2003 He was elected a Fellow of the American Physical Society, and in 2012 became a fellow of the American Mathematical Society.

He received the Doctor Honoris Causa degree from the Universidad Rey Juan Carlos, Madrid, Spain, in January 2014. In June 2014, he received the Doctor Honoris Causa degree from Le Havre University, Le Havre, France. He was a 2016 Thomson Reuters Citations Laureate in Physics.

Contributions

Period three implies chaos

He and his co-author T.Y. Li coined the mathematical term chaos in a paper they published in 1975 entitled Period three implies chaos, in which it was proved that every one-dimensional continuous map

F: R → R

that has a period-3 orbit must have two properties:

(1) For each positive integer p, there is a point in R that returns to where it started after p applications of the map and not before.

This means there are infinitely many periodic points (any of which may or may not be stable): different sets of points for each period p. This turned out to be a special case of Sharkovskii's theorem.

The second property requires some definitions. A pair of points x and y is called “scrambled” if as the map is applied repeatedly to the pair, they get closer together and later move apart and then get closer together and move apart, etc., so that they get arbitrarily close together without staying close together. The analogy is to an egg being scrambled forever, or to typical pairs of atoms behaving in this way. A set S is called a scrambled set if every pair of distinct points in S is scrambled. Scrambling is a kind of mixing.

(2) There is an uncountably infinite set S that is scrambled.

A map satisfying Property 2 is sometimes called "chaotic in the sense of Li and Yorke". Property 2 is often stated succinctly as their article's title phrase "Period three implies chaos". The uncountable set of chaotic points may, however, be of measure zero (see for example the article Logistic map), in which case the map is said to have unobservable nonperiodicity or unobservable chaos.

O.G.Y control method

He and his colleagues (Edward Ott and Celso Grebogi) had shown with a numerical example that one can convert a chaotic motion into a periodic one by a proper time-dependent perturbation of the parameter. This article is considered a classic among the works in the control theory of chaos, and their control method is known as the O.G.Y. method.

Books

Together with Kathleen T. Alligood and Tim D. Sauer, he was the author of the book Chaos: An Introduction to Dynamical Systems.

References

1. "APS Fellow Archive". APS. Retrieved 17 September 2020.
2. List of Fellows of the American Mathematical Society, retrieved 2013-09-01
3. Doctor Honoris Causa degree from the Universidad Rey Juan Carlos, Madrid, Spain, archived from the original on 2018-06-15, retrieved 2017-07-25
4. Doctor Honoris Causa degree from Le Havre University, Le Havre, France
5. Thomson Reuters Citations Laureate in Physics
6. T.Y. Li, and J.A. Yorke, Period Three Implies Chaos, American Mathematical Monthly 82, 985 (1975).
7. Sharkovskii, A. N. (1964). "Co-existence of cycles of a continuous mapping of the line into itself". Ukrainian Math. J. 16: 61–71.
8. Blanchard, F.; Glasner, E.; Kolyada, S.; Maass, A. (2002). "On Li–Yorke pairs". Journal für die reine und angewandte Mathematik. 547: 51–68.
9. Akin, E.; Kolyada, S. (2003). "Li–Yorke sensitivity". Nonlinearity. 16 (4): 1421–1433. Bibcode:2003Nonli..16.1421A. doi:10.1088/0951-7715/16/4/313. S2CID 250751553.
10. Collet, Pierre; Eckmann, Jean-Pierre (1980). Iterated Maps on the Interval as Dynamical Systems. Birkhäuser. ISBN 3-7643-3510-6.

External links

• Website at the University of Maryland
• James A. Yorke at the Mathematics Genealogy Project

v t e Chaos theory
Concepts	Core Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy Theorems Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem
Theoretical branches	Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos
Chaotic maps (list)	Discrete Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map Continuous Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator
Physical systems	Chua's circuit Convection Double pendulum Elastic pendulum FPUT problem Hénon–Heiles system Kicked rotator Multiscroll attractor Population dynamics Swinging Atwood's machine Tilt-A-Whirl Weather
Chaos theorists	Michael Berry Rufus Bowen Mary Cartwright Chen Guanrong Leon O. Chua Mitchell Feigenbaum Peter Grassberger Celso Grebogi Martin Gutzwiller Brosl Hasslacher Michel Hénon Svetlana Jitomirskaya Bryna Kra Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Hee Oh Edward Ott Henri Poincaré Itamar Procaccia Mary Rees Otto Rössler David Ruelle Caroline Series Yakov Sinai Oleksandr Mykolayovych Sharkovsky Nina Snaith Floris Takens Audrey Terras Mary Tsingou Marcelo Viana Amie Wilkinson James A. Yorke Lai-Sang Young
Related articles	Butterfly effect Complexity Edge of chaos Predictability Santa Fe Institute

• 1941 births
• Living people
• 20th-century American mathematicians
• 21st-century American mathematicians
• Chaos theorists
• Columbia University alumni
• Fellows of the American Physical Society
• Fellows of the American Mathematical Society
• Theoretical physicists
• University of Maryland, College Park alumni
• University of Maryland, College Park faculty
• Fellows of the Society for Industrial and Applied Mathematics
• People from Plainfield, New Jersey
• Mathematicians from New Jersey