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This article is cited in 42 scientific papers (total in 42 papers)
Nonremovable Zero Lyapunov Exponents
A. S. Gorodetskiab, Yu. S. Ilyashenkocad, V. A. Kleptsyneaf, M. B. Nalskye a Independent University of Moscow
b California Institute of Technology
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
d Cornell University
e M. V. Lomonosov Moscow State University
f CNRS — Unit of Mathematics, Pure and Applied
Abstract:
Skew products over a Bernoulli shift with a circle fiber are studied. We prove that in the space of such products there exists a nonempty open set of mappings each of which possesses an invariant ergodic measure with one of the Lyapunov exponents equal to zero. The conjecture that the space of $C^2$-diffeomorphisms of the $3$-dimensional torus into itself has a similar property is discussed.
Keywords:
Lyapunov exponent, partially hyperbolic system, nonuniform hyperbolicity, dynamical system, skew product, Bernoulli diffeomorphism.
Received: 24.05.2004
Citation:
A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, “Nonremovable Zero Lyapunov Exponents”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 27–38; Funct. Anal. Appl., 39:1 (2005), 21–30
Linking options:
https://www.mathnet.ru/eng/faa29https://doi.org/10.4213/faa29 https://www.mathnet.ru/eng/faa/v39/i1/p27
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