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Revista Politécnica

On-line version ISSN 2477-8990Print version ISSN 1390-0129


GAVILAN, Maruja. Dinamically Gradient Semigroups in a Metric Space. Rev Politéc. (Quito) [online]. 2022, vol.50, n.1, pp.43-54. ISSN 2477-8990.

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.

Keywords : Lyapunov functions and stability; Attractors; Repellers; Dinamically Gradient Semigroup; 2020 Mathematics Subject Classification; 37B25 (35B41; 37C70; 37B55; 37L05).

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