Phase-locking for dynamical systems on the torus and perturbation theory for Mathieu-type problems

DOI10.1007/BF02430630zbMath0797.58072MaRDI QIDQ1321621

O. G. Galkin

Publication date: 11 October 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

dynamical systemsphase-lockingNewton polyhedronresonanceoscillatorstrigonometric polynomialpartial phase

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items

Resonances and Phase Locking Phenomena for Foliation Preserving Torus Maps ⋮ Stability of an \([N/2\)-dimensional invariant torus in the Kuramoto model at small coupling] ⋮ Boundary of two frequency behaviour in a system of three weakly coupled electronic oscillators ⋮ Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Resonance regions for Mathieu type dynamical systems on a torus
• Bifurcations and stability of families of diffeomorphisms
• Attractors on an N-torus: Quasiperiodicity versus chaos
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Three-frequency quasiperiodicity, phase locking, and the onset of chaos
• On the nature of turbulence
• The nonlinear dynamics of the damped and driven Toda chain. II: Fourier and Lyapunov analysis of tori
• Scaling of the Arnold tongues
• Resonance Zones in Two-Parameter Families of Circle Homeomorphisms
• Rotation Sets of Toral Flows
• Rotation Sets for Maps of Tori
• Resonance regions for families of torus maps