Dissipative flows, global attractors and shape theory
Dynamical Systems
2020-03-18 v1
Abstract
In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the observation that, in general, global attractors are not robust, in the sense that small perturbations of the flow can destroy their globality. We give a necessary and sufficient condition for a global attractor to be continued to a global attractor. We also study, using shape theoretical methods and the Conley index, the bifurcation global to non-global.
Keywords
Cite
@article{arxiv.1802.05704,
title = {Dissipative flows, global attractors and shape theory},
author = {Héctor Barge and José M. R. Sanjurjo},
journal= {arXiv preprint arXiv:1802.05704},
year = {2020}
}
Comments
14 pages, 1 figure. Final version to appear in Top. Appl