Hausdorff dimension, strong hyperbolicity and complex dynamics
This paper is roughly divided into three parts. In the first part the authors give sufficient conditions on an Axiom A surface diffeomorphism that possesses a unique Gibbs measure whose Hausdorff dimension is equal to the Hausdorff dimension of its nonwandering set. In the second part the authors introduce the notion of strong Axiom A diffeomorphisms of a manifold with \(n= \dim M> 2\) and show that the notion of strong hyperbolicity is structurally stable. In the third part they study the dynamics of some proper polynomial maps \(f: \mathbb{C}^2\to \mathbb{C}^2\) which extend to holomorphic self-maps of \(\mathbb{C} P^2\).
scientific article; zbMATH DE number 1492533