Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
نویسندگان
چکیده
منابع مشابه
Almost periodic Szego cocycles with uniformly positive Lyapunov exponents
We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.
متن کاملOn Lyapunov Exponents of Continuous Schrödinger Cocycles over Irrational Rotations
In this note, we consider continuous, SL(2,R)-valued, Schrödinger cocycles over irrational rotations. We prove two generic results on the Lyapunov exponents which improve the corresponding ones contained in [3].
متن کاملLyapunov Exponents For Some Quasi-Periodic Cocycles
We consider SL(2,R)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ± logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. Consider an area preserving diffeomorphism f of a compact surface. Assume that f is not uniformly hyperbolic, but that it has o...
متن کامل- Generic Cocycles Have One - Point Lyapunov Spectrum
We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.
متن کاملProperties of Lyapunov Exponents for Quasiperodic Cocycles with Singularities
We consider the quasi-periodic cocycles (ω, A(x, E)) : (x, v) 7→ (x+ω, A(x, E)v) with ω Diophantine. Let M2(C) be a normed space endowed with the matrix norm, whose elements are the 2 × 2 matrices. Assume that A : T × E → M2(C) is jointly continuous, depends analytically on x ∈ T and is Hölder continuous in E ∈ E , where E is a compact metric space and T is the torus. We prove that if two Lyapu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2008
ISSN: 0003-486X
DOI: 10.4007/annals.2008.167.643