On the failure of linearization for germs of $C^1$ hyperbolic vector fields in dimension one
Dynamical Systems
2023-11-07 v2
Abstract
We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, and settings.
Cite
@article{arxiv.2212.13646,
title = {On the failure of linearization for germs of $C^1$ hyperbolic vector fields in dimension one},
author = {Hélène Eynard-Bontemps and Andrés Navas},
journal= {arXiv preprint arXiv:2212.13646},
year = {2023}
}
Comments
23 pages, minor modifications according to referee's and editor's request. To appear in Journal of Dynamics and Differential Equations