Lyapunov exponents, recurrence, and cusps

报告人： Jorge Olivares-Vinales (SCMS)

摘要： Lyapunov exponents play an important role in studying the ergodic behavior of dynamical systems. In particular, in the seminal work of Pesin, the existence and positivity of Lyapunov exponents were used to study the dynamics of non-uniformly hyperbolic systems. Since then, several extensions of this work have been developed for one-dimensional maps.

In this talk, we show that these ideas cannot be extended to continuous piecewise differentiable interval maps with a finite number of non-flat critical points and Lorenz-like singularities. In this setting, the existence of the Lyapunov exponents depends on the recurrence of the singular set.

时间： 16:00, Thur., 24th October 2024

地点： Room 1210, SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai