New equilibria of non-autonomous discrete dynamical systems

Navascués, M.A. (Universidad de Zaragoza)

Resumen: In the framework of non-autonomous discrete dynamical systems in metric spaces, we propose new equilibrium points, called quasi-fixed points, and prove that they play a role similar to that of fixed points in autonomous discrete dynamical systems. In this way some sufficient conditions for the convergence of iterative schemes of type [fórmula] in metric spaces are presented, where the maps [fórmula] are contractivities with different fixed points. The results include any reordering of the maps, even with repetitions, and forward and backward directions. We also prove generalizations of the Banach fixed point theorems when the self-map is substituted by a sequence of contractivities with different fixed points. The theory presented links the field of dynamical systems with the theory of iterated function systems. We prove that in some cases the set of quasi-fixed points is an invariant fractal set. The hypotheses relax the usual conditions on the underlying space for the existence of invariant sets in countable iterated function systems.

Idioma: Inglés

DOI: 10.1016/j.chaos.2021.111413

Año: 2021

Publicado en: Chaos, Solitons and Fractals 152 (2021), 111413 [8 pp.]
ISSN: 0960-0779

Factor impacto JCR: 9.922 (2021)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 1 / 108 = 0.009 (2021) - Q1 - T1
Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 7 / 86 = 0.081 (2021) - Q1 - T1
Categ. JCR: PHYSICS, MATHEMATICAL rank: 1 / 56 = 0.018 (2021) - Q1 - T1

Factor impacto CITESCORE: 9.9 - Mathematics (Q1) - Physics and Astronomy (Q1)

Factor impacto SCIMAGO: 1.647 - Applied Mathematics (Q1) - Statistical and Nonlinear Physics (Q1) - Mathematics (miscellaneous) (Q1)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)