Invariant structures and multifractal measures in 2d mixing systems

This article analyzes the relationship between geometric invariant structures in two-dimensional mixing systems and measure-theoretical properties associated with the spatial distribution of stable/unstable manifolds of periodic points. Specifically, a connection is established between the Bowen measure associated with the spatial distribution of periodic points and the w-measures characterizing the distribution of stable/unstable leaves throughout the mixing space. This result is made possible through the introduction of the concept of symmetric product of two measures.