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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Geometry of limit sets for expansive Markov systems


Authors: Katrin Gelfert and Michał Rams
Journal: Trans. Amer. Math. Soc. 361 (2009), 2001-2020
MSC (2000): Primary 37E05, 28A78, 57R30
Published electronically: November 3, 2008
MathSciNet review: 2465827
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Abstract: We describe the geometric and dynamical properties of expansive Markov systems.


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Additional Information

Katrin Gelfert
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
Address at time of publication: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Email: gelfert@pks.mpg.de

Michał Rams
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
Email: m.rams@impan.gov.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04759-4
PII: S 0002-9947(08)04759-4
Keywords: Iterated function systems, exceptional minimal sets, thermodynamical formalism, non-uniformly hyperbolic systems, Hausdorff dimension
Received by editor(s): May 7, 2007
Published electronically: November 3, 2008
Additional Notes: The first author’s research was supported by Grant EU FP6 ToK SPADE2
The second author was supported by Grant EU FP6 ToK SPADE2 and by the Polish KBN Grant No 2P0 3A 034 25. Both authors are grateful for discussions with J. Rodriguez-Hertz that led us to Corollary \ref{cor:uh}.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.