This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-11,
author = {M. A. Mor\'on and J. J. S\'anchez-Gabites and J. M. R. Sanjurjo},
title = {Topology and dynamics of unstable attractors},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {239-252},
zbl = {1136.54024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-11}
}
M. A. Morón; J. J. Sánchez-Gabites; J. M. R. Sanjurjo. Topology and dynamics of unstable attractors. Fundamenta Mathematicae, Tome 193 (2007) pp. 239-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm197-0-11/