Mathematical Research Letters
Volume 11 (2004)
SRB measures for Axiom A endomorphisms
Pages: 785 – 797
Let $\Lambda$ be a basic set of an Axiom A endomorphism $f$ on a $n$-dimensional compact Riemannian manifold. In this paper, we provide equivalent conditions for the existence of an SRB measure on $\Lambda$. In particular, we show that under the assumption that the closure of the postcritical set of $f$ is disjoint from $\Lambda$, the existence of an SRB measure is equivalent to the condition that the stable set of $\Lambda$ has packing dimension $n$. Our approach uses the theory of thermodynamic formalism. In particular, we consider the topological pressure on the inverse limit space.