Equicontinuity on semi-locally connected spaces
Dynamical Systems
2015-07-27 v1
Abstract
We show that a homeomorphism of a semi-locally connected compact metric space is equicontinuous if and only if the distance between the iterates of a given point and a given subcontinuum (not containing that point) is bounded away from zero. This is false for general compact metric spaces. Moreover, homeomorphisms for which the conclusion of this result holds satisfy that the set of automorphic points contains those points where the space is not semi-locally connected.
Cite
@article{arxiv.1507.06817,
title = {Equicontinuity on semi-locally connected spaces},
author = {C. A. Morales},
journal= {arXiv preprint arXiv:1507.06817},
year = {2015}
}
Comments
6 pages