GÉNÉRICITÉ D'EXPOSANTS DE LYAPUNOV NON-NULS POUR DES PRODUITS DÉTERMINISTES DE MATRICES GENERICITY OF NON-ZERO LYAPUNOV EXPONENTS FOR DETERMINISTIC PRODUCTS OF MATRICES

By C. Bonatti, X. Gómez-Mont, Marcelo Viana. 2003

111 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a49cf90c64bcc5ec023b7bf96db50bd9822ecec2

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Citations in the corpus

Uniformly Hyperbolic Finite-Valued SL(2,R)-Cocycles (2008, methodology): “Starting from the fundamental work of Furstenberg [9], control of Lyapunov exponents has been obtained in several more general settings: see [11], [10], [4], [5].”
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.”
C1 density of stable ergodicity (2017, background): “ch satisfy: (7) Hs(x;y) = lim n!+1 A 1(y):::A(˙n(y)) 1A(˙n(x)):::A(x): The following is a particular case (for the measure of maximal entropy) of the criterion for non-degenerate Lyapunov spectrum in [BGV]. Theorem 5.2 (Bonatti - Gomez-Mont - Viana). Assume that the cocycle (˙;A) has stable and unst”
Chapter 2 – Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics (2006, background): “In [39], Bonatti, Gómez-Mont and Viana showed that the maximal Lyapunov exponent of μ, χμ, is zero only in the following very special situation: there exists a continuous family of probability measures mx, x ∈ Λ, on the projective space”
Physical measures and absolute continuity for one-dimensional center direction (2013, methodology): “(See Pugh, Viana and Wilkinson [51].)”
Lyapunov exponents for random perturbations of some area-preserving maps including the standard map (2017, background): “, [BV04], [BGMV03]), with a generalization to deterministic maps [AV10].”
Lyapunov exponents with multiplicity 1 for deterministic products of matrices (2004, methodology): “In this setting, it was proved in [11] that an explicit condition about the cocycle over some periodic point and some homoclinic orbit associated to it suffices to ensure the existence of at least one non-zero Lyapunov exponent.”
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”
Diffeomorphisms with positive metric entropy (2014, background): “ne analogously the unstable holonomies Hu(x;y). We now give a condition for deducing the existence of stable holonomies. DIFFEOMORPHISMS WITH POSITIVE METRIC ENTROPY 35 Proposition 5.1 (Lemme 1.12 in [BGV]). If there exists C;>0 such that whenever x;y2 belong to the same local stable manifold we ”