Lyapunov exponents with multiplicity 1 for deterministic products of matrices

By C. Bonatti, Marcelo Viana. Ergodic Theory and Dynamical Systems, 2004

113 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3b3a30b70a3f2bb82ee0667e4fdfa5359d5347cd

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Citations in the corpus

On the regularization of conservative maps (2008, background): “While dynamics in the smooth and the low regularity worlds may often seem to be different altogether (compare [10] and [5]), it turns out that their characteristics can be often combined (both in the conservative and the dissipative setting), yielding for instance great flexibility in obtaining inte”
Extremal Lyapunov exponents: an invariance principle and applications (2010, methodology): “Assuming the base dynamics (g, μ) is fairly “chaotic” (hyperbolic, possibly in a non-uniform fashion), there is now a good understanding of such issues as the existence of non-zero Lyapunov exponents (see Bonatti, Gomez-Mont, Viana [14, 43]) or the simplicity of the Lyapunov spectrum (see Avila, Bon”
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture (2005, background): “It is not dicult to see that it must coincide with ˆ m. Thus, the invariant u-state is unique. See also Remark 5.4 in [ BV ].”
Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents (2008, methodology): “1 of [10] shows how, avoiding another positive codimension subset of cocycles, one can find a new periodic point p̄i ∈ Hi, with period κ̄i a multiple of κi, such that all the eigenvalues of Bi(p̄i) are real and distinct.”
Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows (2011, background): “Also important for our proofs here are the results of Avila, Santamaria and Viana [3] for cocycles over volume-preserving partially hyperbolic systems, both linear and smooth.”