Livšic theorem for matrix cocycles over nonuniformly hyperbolic systems.
| Autor: | Zou, Rui, Cao, Yongluo |
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| Zdroj: | Stochastics & Dynamics; Apr2019, Vol. 19 Issue 2, pN.PAG-N.PAG, 12p |
| Abstrakt: | We prove a nonuniformly hyperbolic version of the Livšic-type theorem, with cocycles taking values in G L (m , ℝ). To be more precise, let f ∈ Diff 1 + γ (M) preserving an ergodic hyperbolic measure μ , and A : M → G L (m , ℝ) be Hölder continuous satisfying A (f n − 1 p) ⋯ A (f p) A (p) = Id for each periodic point f n p = p , then there exists a measurable function C : M → G L (m , ℝ) satisfying A (x) = C (f x) ⋅ C (x) − 1 for μ -almost every x ∈ M. [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
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