Robustly invariant sets in fibre contracting bundle flows
Abstract
We provide abstract conditions which imply the existence of a robustly invariant neighbourhood of a global section of a fibre bundle flow. We then apply such a result to the bundle flow generated by an Anosov flow when the fibre is the space of jets (which are described by local manifolds). As a consequence we obtain sets of manifolds (e.g. approximations of stable manifolds) that are left invariant, {\bf for all} negative times, by the flow and its small perturbations. Finally, we show that the latter result can be used to easily fix a mistake recently uncovered in the paper {\em Smooth Anosov flows: correlation spectra and stability}, \cite{BuL}, by the present authors.
Keywords
Cite
@article{arxiv.1210.3791,
title = {Robustly invariant sets in fibre contracting bundle flows},
author = {Oliver Butterley and Carlangelo Liverani},
journal= {arXiv preprint arXiv:1210.3791},
year = {2014}
}
Comments
This is a completely revised version of "Smooth Invariant Cone Fields: Errata Corrige to "Smooth Anosov Flows: Correlation Spectra and Stability"". The change of title reflects the emphasis on new results eventhough the paper still contains an errata to "Smooth Anosov Flows: Correlation Spectra and Stability"