Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence

DOI10.1134/S1560354714050062zbMath1308.70029arXiv1405.1268OpenAlexW3102797098WikidataQ114074882 ScholiaQ114074882MaRDI QIDQ2513996

Stephen Wiggins, Alessandro Fortunati

Publication date: 29 January 2015

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.1268

zbMATH Keywords

Hamiltonian systemsaperiodic time dependenceKolmogorov theorem

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items

Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium ⋮ The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence ⋮ KAM tori and whiskered invariant tori for non-autonomous systems ⋮ Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow ⋮ A Kolmogorov theorem for nearly integrable Poisson systems with asymptotically decaying time-dependent perturbation ⋮ Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations ⋮ The existence of exponentially decreasing solutions to time dependent hyperbolic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An abstract Nash-Moser theorem with parameters and applications to PDEs
• Invariant KAM tori and global stability for Hamiltonian systems
• Kolmogorov theorem and classical perturbation theory
• Compensations in small divisor problems
• Normal form and Nekhoroshev stability for nearly integrable Hamiltonian systems with unconditionally slow aperiodic time dependence
• Convergent series expansions for quasi-periodic motions
• KAM stability and celestial mechanics
• Generalized implicit function theorems with applications to some small divisor problems, II
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
• Majorant series convergence for twistless KAM tori
• Tree expansion and multiscale analysis for KAM tori
• Improved estimates on the existence of invariant tori for Hamiltonian systems
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

This page was built for publication: Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence