Robustly invariant sets in fiber contracting bundle flows

Oliver Butterley; Carlangelo Liverani

doi:10.3934/jmd.2013.7.255

Article Contents

2013, Volume 7, Issue 2: 255-267. Doi: 10.3934/jmd.2013.7.255

This issue Previous Article Infinitely many lattice surfaces with special pseudo-Anosov maps Next Article Growth of quotients of groups acting by isometries on Gromov-hyperbolic spaces

Robustly invariant sets in fiber contracting bundle flows

Oliver Butterley^1, and
Carlangelo Liverani^2,

1.
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien
2.
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma

Received: September 30, 2012

Published: August 2013

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Abstract

We provide abstract conditions which imply the existence of a robustly invariant neighborhood of a global section of a fiber bundle flow. We then apply such a result to the bundle flow generated by an Anosov flow when the fiber 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 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 Smooth Anosov flows: correlation spectra and stability [2] by the present authors.

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Mathematics Subject Classification: Primary: 37C30; Secondary: 37D30, 37M25.

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References

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