Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles-Reference-Cited by-同舟云学术

Density of positive Lyapunov exponents for 𝑆𝐿(2,ℝ)-cocycles

Published:2011-04-08 Issue:4 Volume:24 Page:999-1014
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Avila Artur

Abstract

We show that S L ( 2 , R ) \mathrm {SL}(2,\mathbb {R}) -cocycles with a positive Lyapunov exponent are dense in all regularity classes and for all non-periodic dynamical systems. For Schrödinger cocycles, we show prevalence of potentials for which the Lyapunov exponent is positive for a dense set of energies.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2011-24-04/S0894-0347-2011-00702-9/S0894-0347-2011-00702-9.pdf

Reference22 articles.

1. Density of positive Lyapunov exponents for quasiperiodic 𝑆𝐿(2,ℝ)-cocycles in arbitrary dimension;Avila, Artur;J. Mod. Dyn.,2009

2. On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators;Avila, Artur;Comm. Math. Phys.,2009

3. [A3] Avila, A., On the Kotani-Last and the Schrödinger Conjectures. In preparation.

4. A formula with some applications to the theory of Lyapunov exponents;Avila, Artur;Israel J. Math.,2002

5. Generic singular spectrum for ergodic Schrödinger operators;Avila, Artur;Duke Math. J.,2005

Cited by 29 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Upper Bound on the Regularity of the Lyapunov Exponent for Random Products of Matrices;Communications in Mathematical Physics;2023-08-08

2. An Invitation to $$SL_2(\mathbb {R})$$ Cocycles Over Random Dynamics;New Trends in Lyapunov Exponents;2023

3. Lyapunov Exponents for Linear Homogeneous Differential Equations;New Trends in Lyapunov Exponents;2023

4. Parameter Spaces of Locally Constant Cocycles;International Mathematics Research Notices;2021-05-25

5. Random product of quasi-periodic cocycles;Proceedings of the American Mathematical Society;2021-04-07