 New equilibria of non-autonomous discrete dynamical systemsM.A. Navascués Chaos, Solitons & Fractals, 2021, vol. 152, issue C Abstract: 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 xk+1=Tkxk in metric spaces are presented, where the maps Tk 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. Keywords: Non-autonomous dynamical systems; Discrete-time systems; Fractals; Iterated function systems; Convergence of numerical algorithms (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007670 DOI: 10.1016/j.chaos.2021.111413 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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