Polynomial maps with hidden complex dynamics

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

4 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)2941-2954
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number6
Publication statusPublished - Jun 2019

Abstract

The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.

Research Area(s)

  • Attractor, bifurcation, Li-Yorke chaos, polynomial map, Smale horseshoe, GENERALIZED HENON MAPS, LORENZ, DIFFEOMORPHISMS