Universal transition in a dynamical system forced at two incommensurate frequencies

DOI10.1016/0167-2789(84)90443-3zbMath0599.70036OpenAlexW2098625667MaRDI QIDQ1080681

James P. Sethna, Eric D. Siggia

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0167-2789(84)90443-3

zbMATH Keywords

stable curvescalingtransition to chaoschaotic statetornado like attractorlow- frequency power spectramode locked statemulticritical parameter valuesrenormalisation group treatmentsaddle-node transitionstable invariant curveunstable invariant curve

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Bifurcations and instability for nonlinear problems in mechanics (70K50)

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Quasiperiodically forced dynamical systems with strange nonchaotic attractors, The nonlinear dynamics of the damped and driven Toda chain. II: Fourier and Lyapunov analysis of tori, Doubling bifurcations of destroyed \(\mathbb{T}^ 2\) tori, A new route to chaos: Sequences of topological torus bifurcations, Intermittency and strange nonchaotic attractors in quasi-periodically forced circle maps., Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos, Strange attractors that are not chaotic

Cites Work

• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
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• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Critical Behavior of a KAM surface. I: Empirical results