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. 
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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/

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