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- W2802395346 abstract "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–Neĭmark–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 Hénon-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 Hénon-like attractors or which can be formed when the saddle-point of a Hénon-like attractor becomes a source." @default.
- W2802395346 created "2018-05-17" @default.
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- W2802395346 date "2018-04-01" @default.
- W2802395346 modified "2023-09-24" @default.
- W2802395346 title "Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps" @default.
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- W2802395346 doi "https://doi.org/10.1142/s0218127418300124" @default.
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