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Funktsional'nyi Analiz i ego Prilozheniya, 2007, Volume 41, Issue 4, Pages 30–45
DOI: https://doi.org/10.4213/faa2877 (Mi faa2877) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Stability of Existence of Nonhyperbolic Measures for $C^1$-Diffeomorphisms

V. A. Kleptsynabcd, M. B. Nalskyab

a M. V. Lomonosov Moscow State University
b Independent University of Moscow
c CNRS — Unit of Mathematics, Pure and Applied
d University of Geneva
Full-text PDF (275 kB) Citations (26)
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DOI: https://doi.org/10.4213/faa2877
Abstract: In the space of diffeomorphisms of an arbitrary closed manifold of dimension $\ge3$, we construct an open set such that each diffeomorphism in this set has an invariant ergodic measure with respect to which one of the Lyapunov exponents is zero. These diffeomorphisms are constructed to have a partially hyperbolic invariant set on which the dynamics is conjugate to a soft skew product with fiber the circle. It is the central Lyapunov exponent that proves to be zero in this case, and the construction is based on an analysis of properties of the corresponding skew products.
Keywords: Lyapunov exponent, partial hyperbolicity, dynamical system, skew product.
Received: 10.04.2006
English version:
Functional Analysis and Its Applications, 2007, Volume 41, Issue 4, Pages 271–283
DOI: https://doi.org/10.1007/s10688-007-0025-8
Bibliographic databases:
Document Type: Article
UDC: 519.987.5+517.938.5
Language: Russian
Citation: V. A. Kleptsyn, M. B. Nalsky, “Stability of Existence of Nonhyperbolic Measures for $C^1$-Diffeomorphisms”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 30–45; Funct. Anal. Appl., 41:4 (2007), 271–283
Citation in format AMSBIB
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    Erratum
    This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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