Hausdorff Dimension of Sets of Generic Points for Non-statistical Dynamical Systems

2025/08/29 by Coates, Douglas, Gelfert, Katrin
#37A05 #37C45 37A05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.00241

Abstract

We consider one dimensional maps with several neutral fixed points that do not admit any physical measures. We show that there is simplex of measures so that every measure in this simplex has a basin which has full Hausdorff dimension.

Citations

• Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points
• Historic behaviour vs. physical measures for irrational flows with multiple stopping points
• Non-statistical rational maps
• Multifractal analysis of non-uniformly hyperbolic systems
• Topological entropy for divergence points
• Metric stability for random walks (with applications in renormalization theory)
• On the variational principle for the topological entropy of certain non-compact sets
• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Topological entropy for noncompact sets

Related

• Hausdorff dimension of particularly non-normal numbers in dynamical systems fulfilling the specification property
• Exceptional sets in homogeneous spaces and Hausdorff dimension
• Natural measures and statistical properties of non-statistical maps with multiple neutral fixed points
• Generic Points of shift-Invariant Measures in the Countable Symbolic Space
• Hausdorff dimension in quasiregular dynamics