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Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition

Published online by Cambridge University Press:  22 June 2007

FRANZ HOFBAUER ,
PETER RAITH  and
KÁROLY SIMON
FRANZ HOFBAUER
Affiliation:
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria (e-mail: franz.hofbauer@univie.ac.at, peter.raith@univie.ac.at)
PETER RAITH
Affiliation:
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria (e-mail: franz.hofbauer@univie.ac.at, peter.raith@univie.ac.at)
KÁROLY SIMON
Affiliation:
Institute of Mathematics, Technical University of Budapest, 1521 Budapest, Pf. 91, Hungary (e-mail: simonk@math.bme.hu)
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Abstract

In this paper some families of skew product self-maps $F$ on the square are considered. The main example is a family forming a two-dimensional analogue of the tent map family. According to the assumptions made in this paper these maps are almost injective. This means that the points of the attractor having more than one inverse image form a set of measure zero for all interesting measures. It may be that $F$ does not have a finite Markov partition. The Hausdorff dimension of the attractor is computed.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1143 - 1165
Copyright
2007 Cambridge University Press

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