Morse decomposition, attractors and chain recurrence


  • José Ayala-Hoffmann Iowa State University.
  • Patrick Corbin Tulane University.
  • Kelly McConville St. Olaf College.
  • Fritz Colonius Universität Augsburg.
  • Wolfgang Kliemann Iowa State University.
  • Justin R. Peters Iowa State University.



Morse decomposition, attractors, repellers, chains, invariants, descomposición Morse, atractores, repulsores, cadenas, invariantes.


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.

Author Biographies

José Ayala-Hoffmann, Iowa State University.

Department of Mathematics.

Patrick Corbin, Tulane University.

Mathematics Department.

Kelly McConville, St. Olaf College.

Department of Mathematics.

Fritz Colonius, Universität Augsburg.

Institut für Mathematik.

Wolfgang Kliemann, Iowa State University.

Department of Mathematics.

Justin R. Peters, Iowa State University.

Department of Mathematics.


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How to Cite

J. Ayala-Hoffmann, P. Corbin, K. McConville, F. Colonius, W. Kliemann, and J. R. Peters, “Morse decomposition, attractors and chain recurrence”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 79-109, May 2017.




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