Title: Counting Pollicott-Ruelle resonances for Axiom A flows

Speaker: 金龙教授（清华大学）

Time: 17:00-18:00, 10th, April, 2024

Place: 五教 5207

Abstract: In 1980's, Pollicott and Ruelle independently introduced the concept of resonances for hyperbolic dynamical systems, for example, Smale's Axiom A flows. They are the poles of the meromorphic continuation of the Laplace transform of the correlation function and thus connected to the mixing property of the system. They are also closely related to the zeros and poles of the dynamical zeta function which is connected to the distribution of periods for closed orbits in the system. In the special cases of Anosov flows, their distributions have been well studied since the work of Faure-Sjostrand in 2010. In this talk, we present the first counting result on Pollicott-Ruelle resonances for general Axiom A flows satisfying strong transversal condition. In particular, we give a polynomial upper bound and a sublinear lower bound on the number of resonances in strips. This is based on joint work with Tao Zhongkai.