We study the complexity of the flow in the region of attraction of an isolated invariant set. More precisely, we define the instablity depth, which is an ordinal and measures how far an isolated invariant set is from being asymptotically stable within its region of attraction. We provide upper and lower bounds of the instability depth in certain cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-2-1,
author = {Konstantin Athanassopoulos},
title = {Remarks on the region of attraction of an isolated invariant set},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {157-167},
zbl = {1087.37014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-2-1}
}
Konstantin Athanassopoulos. Remarks on the region of attraction of an isolated invariant set. Colloquium Mathematicae, Tome 106 (2006) pp. 157-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-2-1/