WIAS Preprint No. 208, (1995)

A dimension formula for endomorphisms - The Belykh family



Authors

  • Schmeling, Jörg
    ORCID: 0000-0001-6956-9463

2010 Mathematics Subject Classification

  • 58F11 58F12

Keywords

  • Hausdorff dimension, invertibility

Abstract

In [11] we considered a class of hyperbolic endomorphisms and asked the question whether there exists a physical motivated invariant measure (SRB-measure) and if so we gave a criterion when the map is invertible on a set of full measure. In this work we want to consider a particular example of this class - in fact a 3-parameter family of those - and proof that a.s. the criterion is fulfilled. From this it follows that the Young formulae for the Hausdorff dimension of the SRB-measure holds.

Appeared in

  • Ergodic Theory Dyn. Sys. 18 (1998) no.5, pp. 1283--1309

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