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- W2139997201 abstract "We prove the Livsic Theorem for arbitrary $GL(m,mathbb R)$ cocycles. We consider a hyperbolic dynamical system $f : X to X$ and a Holder continuous function $A: X to GL(m,mathbb R)$. We show that if $A$ has trivial periodic data, i.e. $A(f^{n-1} p) ... A(fp) A(p) = Id$ for each periodic point $p=f^n p$, then there exists a Holder continuous function $C: X to GL(m,mathbb R)$ satisfying $A (x) = C(f x) C(x) ^{-1}$ for all $x in X$. The main new ingredients in the proof are results of independent interest on relations between the periodic data, Lyapunov exponents, and uniform estimates on growth of products along orbits for an arbitrary Holder function $A$." @default.
- W2139997201 created "2016-06-24" @default.
- W2139997201 creator A5064236321 @default.
- W2139997201 date "2008-08-03" @default.
- W2139997201 modified "2023-09-27" @default.
- W2139997201 title "Livsic theorem for matrix cocycles" @default.
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