RT Journal Article
T1 Unstable manifold, Conley index and fixed points of flows
A1 Barge, Héctor
A1 Rodríguez Sanjurjo, José Manuel
AB 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.
PB Elsevier
SN 0022-247X
YR 2014
FD 2014-12-01
LK https://hdl.handle.net/20.500.14352/33640
UL https://hdl.handle.net/20.500.14352/33640
LA eng
NO MINECO
DS Docta Complutense
RD 10 abr 2025