报告题目(3.1)：史逸 Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori
报告题目：Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori
报告摘要：In this talk, we address on the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with splitted stable bundle, the joint integrability of the strong stable and full unstable subbundles implies existence of fine dominated splitting along the weak stable subbundle as well as Lyapunov exponents rigidity. This builds an equivalence bridge between the geometric rigidity (joint integrability) and dynamical spectral rigidity (Lyapunov exponents rigidity) for Anosov diffeomorphisms on tori.
This talk is based on a joint work with A. Gogolev.
报告题目(3.2)：史逸 Topological and smooth classification of Anosov maps on torus
报告题目：Topological and smooth classification of Anosov maps on torus
报告摘要：In this talk, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic points have the same Lyapunov exponents on the stable bundles. As a corollary, if two C^r non-invertible Anosov maps on torus are topologically conjugate, then the conjugacy is C^r-smooth along the stable foliation. Moreover, we show that the smooth conjugacy class of a non-invertible Anosov map on torus is completely determined by the Jacobians of return maps at periodic points.
This is a joint work with Ruihao Gu.