Probabilistic methods in dynamics

Existence and non-existence of Lyapunov exponents for (random) non-hyperbolic dynamical systems

speaker: Yushi Nakano (Tokai University )

abstract: In this talk, I consider the problem of whether the set of points at which Lyapunov exponent fails to exist, called the Lyapunov irregular set, has positive Lebesgue measure. First, I show that surface diffeomorphisms with a robust homoclinic tangency, as well as other several known nonhyperbolic dynamics, has the Lyapunov irregular set of positive Lebesgue measure (joint work with S. Kiriki, X. Li, T. Soma). Such a positive Lebesgue measure set can be constructed both as the time averages exist and do not exist on it. Next, I show that for any smooth dynamical systems, under a certain type of noise, including absolutely continuous additive noise, the Lyapunov irregular set has zero Lebesgue measure and the number of such Lyapunov exponents is finite (joint work with F. Nakamura, H. Toyokawa).

timetable:
Thu 1 Jun, 10:10 - 11:00, Aula Dini
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