The growth of periodic orbits with large support

Abstract

In this paper, we study the role of periodic measures with large support in the sense of density in invariant measures and the exponential growth for systems with periodic shadowing property or periodic approximate product property. These results are more refined versions of the Sigmund’s density result of periodic measures and Bowen’s entropy formula between the growth of periodic measures and entropy. Furthermore, we provide an abstract framework such that the results also hold for general homoclinic classes and shifts with non-uniform structure.