Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow

DOI10.1142/S021812741830015XzbMath1390.37103OpenAlexW2805393218WikidataQ59425556 ScholiaQ59425556MaRDI QIDQ4566427

Alessandro Fortunati, Stephen Wiggins

Publication date: 15 June 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812741830015x

zbMATH Keywords

shallow-waternearly-integrable systemsaperiodic KAM and Nekhoroshev theoremsarbitrary bathymetry

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Uses Software

• Maxima
• Octave

Cites Work

• Unnamed Item
• Unnamed Item
• Effective stability for slow time-dependent near-integrable Hamiltonians and application
• Water waves over a rough bottom in the shallow water regime
• Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations
• Lagrangian transport in geophysical jets and waves. The dynamical systems approach
• A Kolmogorov theorem for nearly integrable Poisson systems with asymptotically decaying time-dependent perturbation
• Exponential stability for time dependent potentials
• Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow
• Travelling waves over an arbitrary bathymetry: a local stability result
• Effective stability and KAM theory
• KAM tori and whiskered invariant tori for non-autonomous systems
• Normal form and Nekhoroshev stability for nearly integrable Hamiltonian systems with unconditionally slow aperiodic time dependence
• Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence