### Impacto

Giraldo, A. and Rodríguez Sanjurjo, José Manuel
(2004)
*Morse-Smale equations of non-saddle decompositions.*
Topology and its Applications, 140
(1).
pp. 69-80.
ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864103003353

## Abstract

The notion of a non-saddle decomposition of a compact ANR is introduced. This notion extends that of a an attractor-repeller pair. Some cohomological properties of non-saddle decompositions are studied. In particular, some inequalities in the spirit of the Morse-Smale equations for attractor-repeller pairs are obtained. These inequalities involve the ranks of the cohomological Conley index and also of a new cohomological invariant introduced here. The notion of a cyclic Morse decomposition is also introduced and it is proved that this kind of decomposition admits filtrations by non-saddle sets. Finally, these filtrations are used to obtain Morse-Smale equations that generalize those of a Morse decomposition.

Item Type: | Article |
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Additional Information: | International Conference on Topology and Its Applications, SEP 02-09, 2000, Ohrid, MACEDONIA |

Uncontrolled Keywords: | Dynamical system; Isolated set; Non-saddle set; Non-saddle filtration; Cyclic Morse decomposition; Shape |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 16820 |

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Deposited On: | 23 Oct 2012 08:42 |

Last Modified: | 07 Feb 2014 09:36 |

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