Geodesic
Nonremovable Zero Lyapunov Exponents
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 27-38

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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. 
@article{FAA_2005_39_1_a2,
     author = {A. S. Gorodetski and Yu. S. Ilyashenko and V. A. Kleptsyn and M. B. Nalsky},
     title = {Nonremovable {Zero} {Lyapunov} {Exponents}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {27--38},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_1_a2/}
}
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A. S. Gorodetski; Yu. S. Ilyashenko; V. A. Kleptsyn; M. B. Nalsky. Nonremovable Zero Lyapunov Exponents. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/FAA_2005_39_1_a2/