Spectrum Rigidity and Joint Integrability for Anosov Systems on Tori - Lecture 2

Explore the global rigidity properties of irreducible Anosov diffeomorphisms on T^d satisfying center bunching conditions in this advanced mathematics lecture. Delve into how joint integrability of strong stable and full unstable subbundles leads to dynamical coherence, full leaf conjugacy, and matching finest dominated splittings. Examine the concept of spectral rigidity in weak stable bundles and its implications for understanding complex dynamical systems. Gain insights into the intricate relationships between geometric and dynamical properties of Anosov diffeomorphisms on tori through rigorous mathematical analysis and proofs.

Yi Shi (Sichuan University), lecture 2