Yulij Ilyashenko, Cornell University
Professor
Ithaca, New York
yulij@math.cornell.edu
Office:
(607) 255-6334
Expert In
Bio/Research
Dynamical systems describe evolutionary processes in the world around us. The theory of these systems stimulated the development of different branches of mathematics like topology, Lie groups theory, theory of automorphic functions and so on. The modern theory of dynamical systems contains two pa...
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Bio/Research
Dynamical systems describe evolutionary processes in the world around us. The theory of these systems stimulated the development of different branches of mathematics like topology, Lie groups theory, theory of automorphic functions and so on. The modern theory of dynamical systems contains two parts: higher and lower dimensional systems. The first part is much larger than the second one. Its major goal, amidst others, is to understand the chaotic behavior of deterministic systems, and, in particular, to explain the hydrodynamical turbulence. One of the major problems in the lower dimensional theory, namely, in the theory of planar differential equations, is the Hilbert's 16th problem: what may be said about number and location of limit cycles of a planar polynomial vector field with components of degree n? This problem still stays unsolved, but motivated a lot of progress in the theory.
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