Morse decomposition, attractors and chain recurrence

José Ayala-Hoffmann, Patrick Corbin, Kelly McConville, Fritz Colonius, Wolfgang Kliemann, Justin Peters


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.

Palabras clave

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


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