Hölder Continuity of the Lyapunov Exponent for Markov Cocycles

Explore the Hölder continuity of Lyapunov exponents in ergodic theory through this 41-minute lecture from the Simons Semester on Dynamics. Delve into the joint research by Aline Melo, Ao Cai, Marcelo Durães, and Silvius Klein, which establishes the joint Hölder continuity of the maximal Lyapunov exponent as a function of both the Markov cocycle and the transition kernel. Gain insights into their novel approach, which offers a more computable Hölder exponent, addressing a significant problem in the field concerning the regularity of Lyapunov exponents as a function of data.