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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.25 no.1 Antofagasta May 2006

http://dx.doi.org/10.4067/S0716-09172006000100006 

 

Proyecciones Journal of Mathematics
Vol. 25, No 1, pp. 79-109, May 2006.
Universidad Católica del Norte
Antofagasta - Chile

 

MORSE DECOMPOSITION, ATTRACTORS AND CHAIN RECURRENCE

 

JOSE AYALA*
Iowa State University, U. S. A.

PATRICK CORBIN
Tulane University, U. S. A.

KELLY MC CONVILLE
St. Olaf College, U. S. A.

FRITZ COLONIUS
Universitat Augsburg, GERMANY

WOLFGANG KLIEMANN and JUSTIN PETERS
Iowa State University, U. S. A.

Correspondencia a :


Abstract

The global behavior of a dynamical system can be described by its Morse decompositions or its attractor and repeller configurations. There is a close relation between these two approaches and also with (maximal) chain recurrent sets that describe the system behavior on finest Morse sets. These sets depend upper semicontinuously on parameters. The connection with ergodic theory is provided through the construction of invariant measures based on chains.


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Jose Ayala-Hoffmann
Department of Mathematics
Iowa State University
Ames
Iowa 50011
U.S.A.

Patrick Corbin
Mathematics Department
Tulane University
New Orleans
LA 70118,
U.S.A.

Kelly McConville
Department of Mathematics
St. Olaf College
Northfield,
MN 55057,
U.S.A.

Fritz Colonius
Institut für Mathematik
Universität Augsburg
86135 Augsburg,
Germany

Wolfgang Kliemann
Department of Mathematics,
Iowa State University
Ames,
Iowa 50011,
U.S.A.

and

Justin Peters
Department of Mathematics
Iowa State University
Ames
Iowa 50011,
U.S.A.

Received : September 2005. Accepted : November 2005

*Partially supported by Proyecto Fondecyt Regular 1020439, Chile
Partially supported by NSF Award DMS-0353880, Research Experience for Undergraduate at Iowa State University.
Partially supported by NSF Award DMS-0353880, Research Experience for Undergraduate at Iowa State University.

 

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