A geometric criterion for adiabatic chaos

DOI10.1063/1.530636zbMath0799.58049OpenAlexW2598717529MaRDI QIDQ4300205

Gregor Kovačič, Tasso J. Kaper

Publication date: 31 July 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530636

zbMATH Keywords

chaosHamiltonian systemsSmale horseshoeadiabatic systems

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (8)

Higher-order Melnikov theory for adiabatic systems ⋮ Adiabatic invariants, diffusion and acceleration in rigid body dynamics ⋮ A NONINTEGRABILITY CRITERION FOR ADIABATIC SYSTEMS ⋮ Frequency spanning homoclinic families. ⋮ Wavenumber transport: scattering of small-scale internal waves by large-scale wavepackets ⋮ Unnamed Item ⋮ Universal properties of chaotic transport in the presence of diffusion ⋮ Finite time transport in aperiodic flows

Cites Work

• Diffusion of particles in a slowly modulated wave
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Lobe area via action formalism in a class of Hamiltonian systems
• Chaos in the Duffing equation
• On the periodic solutions of a forced second-order equation
• A commentary ``On the periodic solutions of a forced second-order equation by S. P. Hastings and J. B. McLeod
• An analytical study of transport in Stokes flows exhibiting large-scale chaos in the eccentric journal bearing
• Slowly Varying Phase Planes and Boundary-Layer Theory
• Flux and differences in action for continuous time Hamiltonian systems
• Resonant sloshing in shallow water
• On the Detection and Dynamical Consequences of Orbits Homoclinic to Hyperbolic Periodic Orbits and Normally Hyperbolic Invariant Tori in a Class of Ordinary Differential Equations
• Slowly pulsating separatrices sweep homoclinic tangles where islands must be small: an extension of classical adiabatic theory
• Diagrammatic theory of transition of pendulum like systems
• Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic

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