Morse decomposition of global attractors with infinite components
Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Abstract: In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, we are able to prove that the gradient dynamics on Morse sets together with a separation assumption is equivalent to the existence of an ordered Lyapunov function associated to the Morse sets and also to the existence of a Morse decomposition -that is, the global attractor can be described as an increasing family of local attractors and their associated repellers.
Keywords: Morse decomposition, infinite components, gradient dynamics, Lyapunov
function, gradient-like semigroup.
Received: December 2013; Revised: December 2014; Available Online: January 2015.
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