Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 3

Explore the third lecture in a minicourse on spectrum rigidity and joint integrability for Anosov systems on tori. Delve into the study of irreducible and non-conformal Anosov automorphisms A ∈ Sp(4, Z) and their symplectic diffeomorphisms. Examine the conditions under which the extremal symplectic bundle of a C^1-close symplectic diffeomorphism f is integrable, and how this relates to smooth conjugacy with A. Gain insights into the rigidity properties of Anosov diffeomorphisms on tori and the connections between geometric rigidity and dynamical spectral rigidity.

Yi Shi (Sichuan University), lecture 3