English

Stable set of self map

Group Theory 2009-09-22 v1 Dynamical Systems

Abstract

The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call \emph{stable set} of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal in the general case. Here we determine whether or not the equality holds in several particular cases, among which are the case of a dense range continuous function on an Hilbert space, and the case of a substitution over left infinite words.

Keywords

Cite

@article{arxiv.0909.3779,
  title  = {Stable set of self map},
  author = {Eddy Godelle},
  journal= {arXiv preprint arXiv:0909.3779},
  year   = {2009}
}
R2 v1 2026-06-21T13:48:41.108Z