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Periodic data conjugacy for diffeomorphism cocycles
Abstract
We consider Hölder continuous cocycles over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold. We focus on establishing conjugacy between two cocycles from conjugacy of their periodic data. We obtain such a result under bunching, or domination, assumption on the cocycles and a mild regularity assumption in C0 topology on the maps conjugating the periodic data. We also obtain conjugacy to a constant cocycle assuming boundedness in C1 or pre-compactness in C0 for the constant cocycle and the conjugating maps.
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BibTeX
@misc{sadovskaya2026periodic,
title = {{Periodic data conjugacy for diffeomorphism cocycles}},
author = {Victoria Sadovskaya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35460},
eprint = {2610.35460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35460},
}
RIS
TY - UNPB
TI - Periodic data conjugacy for diffeomorphism cocycles
AU - Victoria Sadovskaya
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35460
UR - https://arxiv.org/abs/2610.35460
AB - We consider Hölder continuous cocycles over a hyperbolic dynamical system with values in the group of diffeomorphisms of a compact manifold. We focus on establishing conjugacy between two cocycles from conjugacy of their periodic data. We obtain such a result under bunching, or domination, assumption on the cocycles and a mild regularity assumption in C^0 topology on the maps conjugating the periodic data. We also obtain conjugacy to a constant cocycle assuming boundedness in C^1 or pre-compactness in C^0 for the constant cocycle and the conjugating maps.
ER -