Chaos for foliated spaces and pseudogroups
Dynamical Systems
2024-12-09 v3
Abstract
We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, exhibiting a counterexample in the non-compact case. Finally, we obtain an analogue of the Auslander-Yorke dichotomy for compact foliated spaces and compactly generated pseudogroups.
Cite
@article{arxiv.2202.09983,
title = {Chaos for foliated spaces and pseudogroups},
author = {Ramón Barral Lijó},
journal= {arXiv preprint arXiv:2202.09983},
year = {2024}
}
Comments
36 pages, 2 figures. Changes over previous version: minor corrections. Version accepted for publication in Revista Matem\'atica Iberoamericana