Measure of full dimension for some nonconformal repellers

2007/05/24 by Luzia, Nuno
#37C45 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0705.3604

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.

Related

• On the uniqueness of an ergodic measure of full dimension for\n non-conformal repellers
• Dimension Estimates for Non-conformal Repellers and Continuity of Sub-additive Topological Pressure
• Nonadditive Measure-theoretic Pressure and Applications to Dimensions of an Ergodic Measure
• Dimension theoretical study on skew product maps with coupled-expanding property
• New bounds for the Hausdorff dimension of a dynamically defined Cantor\n set