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arXiv · 2012.03314

Ledrappier-Young formulae for a family of nonlinear attractors

Natalia Jurga·Lawrence D. Lee
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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.

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Natalia Jurga, Lawrence D. Lee. 2020-12-06. Ledrappier-Young formulae for a family of nonlinear attractors. https://arxiv.org/abs/2012.03314

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