Dynamics on Hyperspaces
Dynamical Systems
2018-11-12 v1
Abstract
Given a compact metric space (X; \varrho) and a continuous function f:X\rightarrow X, we study the dynamics of the induced map \bar{f} on the hyperspace of the compact subsets of X. We show how the chain recurrent set of f and its components are related with the one of the induced map. The main result of the paper proves that, under mild conditions, the numbers of chain components of \bar{f} is greater than the ones of f. Showing the richness in the dynamics of \bar{f} which cannot be perceived by f.
Cite
@article{arxiv.1811.04034,
title = {Dynamics on Hyperspaces},
author = {Victor Ayala and Adriano Da Silva and Heriberto Roman-Flores},
journal= {arXiv preprint arXiv:1811.04034},
year = {2018}
}