Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 4

Explore the rigidity properties of non-invertible Anosov maps on 2-torus in this fourth lecture of a minicourse on spectrum rigidity and joint integrability for Anosov systems on tori. Delve into the relationship between topological conjugacy and spectral rigidity along stable bundles for these maps. Examine how topological conjugacy implies the existence of identical Lyapunov exponents on corresponding periodic points. Discover the implications of this relationship, including the smoothness of conjugacy along stable foliations. Gain insights into the connections between geometric and dynamical spectral rigidity in the context of Anosov diffeomorphisms on tori.

Yi Shi (Sichuan University), lecture 4