Dynamics of a two-dimensional map on nested circles and rings

Laura Gardini, Iryna Sushko and Fabio Tramontana

Chaos, Solitons & Fractals, 2021, vol. 143, issue C

Abstract: We consider a discrete dynamical system, a two-dimensional real map which represents a one-dimensional complex map. Depending on the parameters, its bounded dynamics can be restricted to an invariant circle, cyclic invariant circles, invariant annular regions or disks. We show that on such invariant sets the trajectories are always either periodic of the same period, or quasiperiodic and dense. Moreover, the invariant sets may be transversely attracting or repelling, and undergo the typical cascade of period doubling bifurcations. Homoclinic bifurcations can also occur, leading to chaotic rings, annular regions filled with dense repelling cyclical circles and aperiodic trajectories.

Keywords: Two-dimensional maps; Dynamics on nested circles and rings; Non standard Neimark-Sacker bifurcation; Linear fractional maps (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309449

DOI: 10.1016/j.chaos.2020.110553

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