Measure of full dimension for some nonconformal repellers

TL;DR

This paper establishes the existence of an ergodic measure with full Hausdorff dimension for certain nonlinear nonconformal skew-product transformations, using a variational principle for topological pressure.

Contribution

It introduces a variational principle for topological pressure on noncompact sets and applies it to prove full dimension measures in nonconformal dynamics.

Findings

Existence of ergodic measure with full Hausdorff dimension

Development of a variational principle for noncompact sets

Application to nonlinear nonconformal skew-product transformations

Abstract

We prove the existence of an ergodic measure with full Hausdorff dimension for a class of nonlinear nonconformal skew-product transformations. In order to do so we establish a variational principle for the topological pressure of certain noncompact sets.