A remark on the invertibility of semiinvertible cocycles
Abstract
We observe that under certain conditions on the Lyapunov exponents a semiinvertible cocycle is, indeed, invertible. As a consequence, if a semiinvertible cocycle generated by a Hölder continuous map $A:M\to M(d, \mathbb{R})$ over a hyperbolic map $f:M\to M$ satisfies a Livšic's type condition, that is, if $A(f^{n1}(p))\cdot\ldots \cdot A(f(p))A(p)=\text{Id}$ for every $p\in \text{Fix}(f^n)$ then the cocycle is invertible, meaning that $A(x)\in GL(d,\mathbb{R})$ for every $x\in M$, and a Livšic's type theorem is satisfied.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 DOI:
 10.48550/arXiv.1709.05373
 arXiv:
 arXiv:1709.05373
 Bibcode:
 2017arXiv170905373B
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 Some corrections to the previous version were made