Ledrappier-Young formulae for a family of nonlinear attractors
Dynamical Systems
2020-12-08 v1 Classical Analysis and ODEs
Metric Geometry
Abstract
We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for H\"older continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier-Young formula.
Keywords
Cite
@article{arxiv.2012.03314,
title = {Ledrappier-Young formulae for a family of nonlinear attractors},
author = {Natalia Jurga and Lawrence D. Lee},
journal= {arXiv preprint arXiv:2012.03314},
year = {2020}
}
Comments
15 pages, 1 figure