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The prize is endowed by and named after Michael Brin, [1] whose son Sergey Brin [2] is a co-founder of Google. Michael Brin is a retired mathematician at the University of Maryland and a specialist in dynamical systems. [3] The first prize was awarded in 2008, between 2009 and 2017 it has been awarded bi-annually, and since 2017 annually.
Many chaotic dynamical systems are isomorphic to subshifts of finite type; examples include systems with transverse homoclinic connections, diffeomorphisms of closed manifolds with a positive metric entropy, the Prouhet–Thue–Morse system, the Chacon system (this is the first system shown to be weakly mixing but not strongly mixing ...
Suspension is a construction passing from a map to a flow.Namely, let be a metric space, : be a continuous map and : + be a function (roof function or ceiling function) bounded away from 0.
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [13]
Hyperbolic equilibrium point p is a fixed point, or equilibrium point, of f, such that (Df) p has no eigenvalue with absolute value 1. In this case, Λ = {p}.More generally, a periodic orbit of f with period n is hyperbolic if and only if Df n at any point of the orbit has no eigenvalue with absolute value 1, and it is enough to check this condition at a single point of the orbit.
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied.