The Hausdorff dimension of measures for iterated function systems which contract on average

Thomas Jordan; Mark Pollicott

doi:10.3934/dcds.2008.22.235

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2008, Volume 22, Issue 1&2: 235-246. Doi: 10.3934/dcds.2008.22.235

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The Hausdorff dimension of measures for iterated function systems which contract on average

Thomas Jordan^1, and
Mark Pollicott^2,

1.
Department of Mthematics, University of Bristol, University Walk, Clifton, Bristol, BS8 1TW
2.
Department of Mathematics, Warwick University, Coventry CV4 7AL

Received: December 31, 2006

Revised: April 30, 2007

Published: February 2008

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Abstract

In this note we consider measures supported on limit sets of systems that contract on average. In particular, we present an upper bound on their Hausdorff dimension.

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Mathematics Subject Classification: Primary: 37L30 and 37H15; secondary: 37C40 and 37M25.

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