The resonance theory for stochastic layers in nonlinear dynamic systems.

DOI10.1016/S0960-0779(00)00225-3zbMath1073.70523OpenAlexW2033459047MaRDI QIDQ1600559

Albert C. J. Luo, Ray P. S. Han

Publication date: 17 June 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(00)00225-3

zbMATH Keywords

integrable Hamiltonian systemwhisker maptwin-well Duffing oscillator

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Dynamical systems in classical and celestial mechanics (37N05) Nonlinear resonances for nonlinear problems in mechanics (70K30)

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Cites Work

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• Transport rates of a class of two-dimensional maps and flows
• The separation of motions in systems with rapidly rotating phase
• External field induced chaos in an infinite square well potential
• Regular and chaotic dynamics.
• A refined formula for the separatrix splitting for the standard map
• Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
• Resonant-separatrix webs in stochastic layers of the twin-well Duffing oscillator
• Splitting of separatrices for standard and semistandard mappings
• Analysis of the separatrix map in Hamiltonian systems
• Chaotic analysis of subharmonic resonant waves in undamped and damped strings
• Width of stochastic layers in near-integrable two-dimensional symplectic maps.
• The accuracy of symplectic integrators
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Exponentially small splittings in Hamiltonian systems
• Secondary homoclinic bifurcation theorems
• An averaging method for Hamiltonian systems, exponentially close to integrable ones
• Homoclinic tangles-classification and applications
• Two-Dimensional Measure-Preserving Mappings

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