Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

• 成果类型: Article
• 署名作者: Viana, Marcelo
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.167.643
• 发表日期: 2008
• 页码: 643-680
• 关键词: deterministic products; RANDOM MATRICES; attractors; simplicity; genericity; PROOF

摘要

We prove that for any s > 0 the majority of C-s linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-infinity. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.