The structure of mode-locked regions in quasi-periodically forced circle maps

DOI10.1016/S0167-2789(99)00235-3zbMath0983.37044OpenAlexW2009919314MaRDI QIDQ1570780

Paul Glendinning, Jaroslav Stark, Ulrike Feudel, Arkadij S. Pikovskij

Publication date: 23 April 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(99)00235-3

zbMATH Keywords

rotation numberArnold circle mapmode-locked regionsquasiperiodically force

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Nonlinear dynamics in mechanics (70K99) Simulation of dynamical systems (37M05) Rotation numbers and vectors (37E45)

Related Items (13)

Jaroslav Stark: 1960–2010 ⋮ Transitive sets for quasi-periodically forced monotone maps ⋮ One-dimensional monotone nonautonomous dynamical systems ⋮ Manifolds on the verge of a hyperbolicity breakdown ⋮ Fine structure of mode-locked regions of the quasi-periodically forced circle map ⋮ Existence of non-smooth bifurcations of uniformly hyperbolic invariant manifolds in skew product systems ⋮ MODE-LOCKING IN QUASIPERIODICALLY FORCED SYSTEMS WITH VERY SMALL DRIVING FREQUENCY ⋮ Abundance of mode-locking for quasiperiodically forced circle maps ⋮ Unwrapping trajectories of a quasi-periodic forced oscillator can give maps of the real line with sna ⋮ Rotation numbers for quasi-periodically forced monotone circle maps ⋮ Rotation numbers for quasiperiodically forced circle maps-mode-locking vs. strict monotonicity ⋮ Strange non-chaotic attractors in quasiperiodically forced circle maps ⋮ Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall

Cites Work

• Unnamed Item
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• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• Strange attractors that are not chaotic
• The birth of strange nonchaotic attractors
• Strange non-chaotic attractor in a quasiperiodically forced circle map
• Locating bifurcations in quasiperiodically forced systems
• Intermittency and strange nonchaotic attractors in quasi-periodically forced circle maps.
• Fine structure of mode-locked regions of the quasi-periodically forced circle map
• Quasiperiodic forcing and the observability of strange nonchaotic attractors
• Characterizing strange nonchaotic attractors

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