A Remark on the Invertibility of Semi-invertible Cocycles View Full Text


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Article Info

DATE

2018-09-20

AUTHORS

Lucas Backes

ABSTRACT

We observe that under certain conditions on the Lyapunov exponents, a semi-invertible cocycle is, indeed, invertible. As a consequence, if a semi-invertible cocycle generated by a Hölder continuous map A:ℳ→M(d,ℝ) over a hyperbolic system f:ℳ→ℳ satisfies a Livšic’s type condition, that is, if A(fn− 1(p)) ⋅… ⋅ A(f(p))A(p) = Id for every p ∈ Fix(fn), then the cocycle is invertible, meaning that A(x)∈GL(d,ℝ) for every x∈ℳ, and a Livšic’s type theorem is satisfied. More... »

PAGES

1-7

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URI

http://scigraph.springernature.com/pub.10.1007/s10883-018-9420-0

DOI

http://dx.doi.org/10.1007/s10883-018-9420-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107125370


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