James A. Yorke

James Alan Yorke ( born August 3, 1941 in Plainfield, New Jersey, USA) is an American professor of physics and mathematics and Chairman of the Mathematics Department of the University of Maryland, College Park.

Life

Yorke went to Pingry School in Martinsville, New Jersey. He studied at Columbia University with a bachelor's degree in 1963 and in 1966 with Aaron Strauss at the University of Maryland Ph.D. in Mathematics ( Asymptotic Properties of Solutions Using the Second Derivative of a Liapunov function) He remained at the University of Maryland, he attended the 1972 research Professorship received. In 1988 he became director of the Institute for Physical Science and Technology.

Yorke is a pioneer of chaos theory. He and his graduate student TY Li coined the mathematical concept of chaos for research direction (the one in mathematics also called qualitative theory of differential equations and dynamical systems theory ). In 1975 in an influential work Period Three Implies Chaos In it, they studied one-dimensional discrete dynamical systems such as square pictures of the unit interval (logistic equation ), which soon thereafter (also because of simultaneous work of Robert May ) a main model for the study of dynamical systems was ( with the discovery of the Feigenbaum period -doubling scenario of chaos formation and its universality late 1970s ). They proved generally that also occur upon the occurrence of periods of the order of 3, all other periods k and initial values ​​with completely chaotic behavior. Li and Yorke had, however, already in 1964, is also known as Sharkovskii 's Theorem a precursor in the work of the Ukrainian mathematician Olexandr Mikolajowytsch Scharkowski ( Sharkovsky ), which is why the sentence that also periods occur with periods of order 3 of each order.

With Celso Grebogi, and Edward Ott 1990 he founded the Research for the control of chaos. He dealt with applications of chaos theory, among others, in Epidemiology.

His doctoral heard Tien- Yien Li (Professor at Michigan State University).

Awards

He is a Fellow of the American Physical Society, the American Mathematical Society and the American Association for the Advancement of Science.

Writings

  • By Kathleen T. Alligood, Tim Sauer chaos. An introduction to dynamical systems, Springer Verlag 1997
  • Publisher Tim Sauer, Edward Ott Coping with chaos, Wiley 1994
  • With T. Y. Li: Period Three Implies Chaos. In: American Mathematical Monthly. Volume 82, 1975, p 985
  • Edward Ott, Celso Grebogi Chaos, strange attractors and fractal basin boundaries in nonlinear dynamical systems, Science, Volume 238, 1987, p 585
  • E. Ott, Grebogi Controlling chaos, Physical Review Letters, Volume 64, 1990, p 1196
  • With T. Shinbrot, Ott, Grebogi Using small perturbations to control chaos, Nature, vol 363, 1993, p 411
Plainfield (New Jersey) Mitchell Feigenbaum Japan Prize Mathematical Association of America Integrated Authority File
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