Research-Some Dynamical and Topological Invariants for symplectic diffeomorphisms

Research

Dynamical Systems Seminar

Some Dynamical and Topological Invariants for symplectic diffeomorphisms

Speaker: Zhihong Xia（Northwestern University）
Time: Oct 18, 2023, 15:00-16:00
Location: M1001, College of Science Building

Abstract

Consider a symplectic diffeomorphism on a compact symplectic manifold. There are two notable invariants, the area and volume flux and mean rotation yector. We show that the volume flux (which is defined as a cohomology element) is exactly the Poincare dual of the rotation vector (a homology element). We also establish the relationships between the area flux and the volume flux, and show that a symplectic diffeomorphism is Hamiltonian if and only if the rotation yector is zero.