Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps

S. Garst, A.E. Sterk

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We study the dynamics of three planar, noninvertible maps which rotate and fold the plane. Two maps are inspired by real-world applications whereas the third map is constructed to serve as a toy model for the other two maps. The dynamics of the three maps are remarkably similar. A stable fixed point bifurcates through a Hopf-Neimark-Sacker which leads to a countably infinite set of resonance tongues in the parameter plane of the map. Within a resonance tongue a periodic point can bifurcate through a period-doubling cascade. At the end of the cascade we detect Henon-like attractors which are conjectured to be the closure of the unstable manifold of a saddle periodic point. These attractors have a folded structure which can be explained by means of the concept of critical lines. We also detect snap-back repellers which can either coexist with Henon-like attractors or which can be formed when the saddle-point of a Henon-like attractor becomes a source.

Originele taal-2English
Aantal pagina's20
TijdschriftInternational Journal of Bifurcation and Chaos
Nummer van het tijdschrift4
StatusPublished - apr.-2018

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