Dinamically Gradient Semigroups in a Metric Space

Gavilán M. · Revista Politecnica (2022) · DOI: 10.33333/rp.vol50n1.05

Resumen

We study the internal dynamics of an invariant compact by using different concepts: local attractor, repeller and “pair attractor-repeller”. The “Decomposition of Morse” (in the sense of Rybakowski (1987)) is described, and on a global attractor we prove the equivalence of the concepts of local attractor and Decomposition of Morse given in the books of Carvalho et al. (2013) and of Rybakowski (1987). The results of Aragão et al. (2011) are presented according to which there exists an equivalence between the gradient semigroup (it has a Lyapunov function) and the dynamically gradient semigroup (in the sense of Carvalho et al. (2013)). We conclude by presenting the stability of gradient semigroups under perturbations, via illustrative examples.

Instituciones: Universidad Nacional Mayor de San Marcos