Non-uniform hyperbolicity of random coupled standard maps

Dynamical Systems Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Svetlana Katok, Kurt Vinhage.

Speaker: Pablo Carrasco, UFMG

Abstract: A central problem in smooth ergodic theory is establishing the existence of positive Lyapunov exponents for conservative surface maps that are hyperbolic in a large but non invariant region of the phase space. The prototypical example exhibiting this behavior is the Chirikov-Taylor standard map family in the two torus, that albeit its apparently simple form, has a extremely complicated dynamics that resists all attempts up to date to prove its (non-uniform) hyperbolicity. Perhaps even more difficult would be establishing the positivity or non-uniform hyperbolicity of systems of coupled standard maps (as for example in the Froeschle family). In this talk I'll consider a random version of these coupled systems and show that in that setting the resulting map is non-uniformly hyperbolic.

Room Reservation Information

Room Number: 114 McAllister

Date: 10/21/2019

Time: 3:40pm - 4:40pm