In 1926 Birkhoff defined the center depth, one of the fundamental invariants that characterize the topological structure of a dynamical system. In this paper, we introduce the concepts of prolongational centers and their depths, which lead to a complete family of topological invariants. Some basic properties of the prolongational centers and their depths are established. Also, we construct a dynamical system in which the depth of a prolongational center is a prescribed countable ordinal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm22-10-2015,
author = {Boyang Ding and Changming Ding},
title = {Prolongational centers and their depths},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {287-296},
zbl = {06602794},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm22-10-2015}
}
Boyang Ding; Changming Ding. Prolongational centers and their depths. Fundamenta Mathematicae, Tome 233 (2016) pp. 287-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm22-10-2015/