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Hausdorff and packing measure for solenoids

Published online by Cambridge University Press:  24 January 2003

MICHAŁ RAMS  and
KÁROLY SIMON
MICHAŁ RAMS
Affiliation:
Michał Rams Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland (e-mail: [email protected])
KÁROLY SIMON
Affiliation:
Institute of Mathematics, Technical University of Budapest, H-1529 PO box 91, Hungary (e-mail: [email protected])
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Abstract

We prove that the solenoid with two different contraction coefficients has zero Hausdorff and positive packing measure in its own dimension and the SBR measure is equivalent to the packing measure on the attractor. Further, we prove similar statements for Slanting Baker maps with intersecting cylinders (in \mathbb{R}^{2}).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 273 - 291
Copyright
2003 Cambridge University Press

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