Counting Pollicott--Ruelle resonances for Axiom A flows

In this paper, we count the number of Pollicott–Ruelle resonances for open hyperbolic systems and Axiom A flows. In particular, we prove polynomial upper bounds and sublinear lower bounds on the number of resonances with modulus less than $r$ in strips for open hyperbolic systems and Axiom A flows with a transversality condition.