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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

 

Lyapunov exponents and other properties of $ N$-groups


Authors: D. A. Filimonov and V. A. Kleptsyn
Translated by: G. G. Gould
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva.
Journal: Trans. Moscow Math. Soc. 2012, 29-36
MSC (2010): Primary 37C85; Secondary 37E10, 37A35, 37D25, 37H15
Published electronically: January 24, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the class of minimally acting finitely generated groups of $ C^2$-diffeomorphisms of the circle which have the property that the nonexpandable points are fixed, where the set of nonexpandable points is nonempty. It turns out that the Lyapunov expansion exponent of any such action is zero. As a consequence, we have a singularity of the stationary measure for a random dynamical system given by any probability distribution whose support is a finite set of the generating elements of the group.


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Additional Information

D. A. Filimonov
Affiliation: Moscow State University
Email: mityafil@gmail.com

V. A. Kleptsyn
Affiliation: CNRS, Institut de Recherche Mathématique de Rennes
Email: victor.kleptsyn@univ-rennes1.fr

DOI: http://dx.doi.org/10.1090/S0077-1554-2013-00198-3
PII: S 0077-1554(2013)00198-3
Keywords: Dynamical systems, group actions, diffeomorphisms of the circle, Lyapunov exponent, stationary measures.
Published electronically: January 24, 2013
Additional Notes: This work was carried out with the partial support of the Russo-French programme “Cooperation network in mathematics”, grant RFFI-10-01-00739-a and grant RFFI-CNRS-10-01-93115-NTsNIL-a.
Article copyright: © Copyright 2013 American Mathematical Society