Ledrappier–Young formulae for a family of nonlinear attractors

Lawrence David Lee, Natalia Anna Jurga

Research output: Contribution to journalArticlepeer-review

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 Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.
Original languageEnglish
Number of pages15
JournalMathematische Zeitschrift
VolumeFirst Online
Early online date4 Oct 2021
DOIs
Publication statusE-pub ahead of print - 4 Oct 2021

Keywords

  • Ledrappier–Young formula
  • Quasi-Bernoulli measure
  • Exact dimensional
  • Non-conformal attractor

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