Unstable manifold, Conley index and fixed points of flows

Barge Yáñez, Héctor and Rodríguez Sanjurjo, José Manuel (2014). Unstable manifold, Conley index and fixed points of flows. "Journal of Mathematical Analysis and Applications", v. 420 (n. 1); pp. 835-851. ISSN 0022-247X. https://doi.org/10.1016/j.jmaa.2014.06.016.

Description

Title: Unstable manifold, Conley index and fixed points of flows
Author/s:
  • Barge Yáñez, Héctor
  • Rodríguez Sanjurjo, José Manuel
Item Type: Article
Título de Revista/Publicación: Journal of Mathematical Analysis and Applications
Date: December 2014
ISSN: 0022-247X
Volume: 420
Subjects:
Freetext Keywords: Unstable manifold; Parallelizable structure; Attractor; Conley index; Non-saddle set; Morse decomposition
Faculty: E.T.S. de Ingenieros Informáticos (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We study dynamical and topological properties of the unstable manifold of isolated invariant compacta of flows. We show that some parts of the unstable manifold admit sections carrying a considerable amount of information. These sections enable the construction of parallelizable structures which facilitate the study of the flow. From this fact, many nice consequences are derived, specially in the case of plane continua. For instance, we give an easy method of calculation of the Conley index provided we have some knowledge of the unstable manifold and, as a consequence, a relation between the Brouwer degree and the unstable manifold is established for smooth vector fields. We study the dynamics of non-saddle sets, properties of existence or non-existence of fixed points of flows and conditions under which attractors are fixed points, Morse decompositions, preservation of topological properties by continuation and classify the bifurcations taking place at a critical point.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2012-30719UnspecifiedUniversidad Complutense de MadridTopología geométrica, topología en dimensión baja y dinámica topológica

More information

Item ID: 45647
DC Identifier: http://oa.upm.es/45647/
OAI Identifier: oai:oa.upm.es:45647
DOI: 10.1016/j.jmaa.2014.06.016
Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X14005630
Deposited by: Memoria Investigacion
Deposited on: 02 Nov 2017 11:34
Last Modified: 02 Nov 2017 11:34
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