On passage through resonances in volume-preserving systems

DOI10.1063/1.2404585zbMath1146.37350arXivnlin/0604047OpenAlexW3105637364WikidataQ51925819 ScholiaQ51925819MaRDI QIDQ3531704

Dmitri Vainchtein, Igor Mezić, Anatoly I. Neishtadt

Publication date: 3 November 2008

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

Full work available at URL: https://arxiv.org/abs/nlin/0604047

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Hamiltonian and Lagrangian mechanics (70H99)

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Cites Work

• Unnamed Item
• Scattering by resonances
• Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave
• Resonances and particle stochastization in nonhomogeneous electromagnetic fields
• Passive scalars, three-dimensional volume-preserving maps, and chaos
• On a class of steady confined Stokes flows with chaotic streamlines
• Chaotic streamlines inside drops immersed in steady Stokes flows
• Electrohydrodynamically driven chaotic mixing in a translating drop. II. Experiments
• Chaotic mixing in thermocapillary-driven microdroplets
• Electrohydrodynamically driven chaotic mixing in a translating drop
• Change of the adiabatic invariant at a separatrix in a volume-preserving 3D system
• Chaotic advection in three-dimensional unsteady incompressible laminar flow
• Geometric and statistical properties induced by separatrix crossings in volume-preserving systems
• Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow
• Adiabatic chaos in a two‐dimensional mapping