Effective stability for slow time-dependent near-integrable Hamiltonians and application

DOI10.1016/j.crma.2013.07.024zbMath1288.37018arXiv1303.5045OpenAlexW2090908712WikidataQ114192289 ScholiaQ114192289MaRDI QIDQ386663

Abed Bounemoura

Publication date: 10 December 2013

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5045

zbMATH Keywords

effective stabilitynonautonomous systemnear-integrable Hamiltonians

Mathematics Subject Classification ID

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

Related Items

Nekhoroshev's estimates for quasi-periodic time-dependent perturbations ⋮ The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence ⋮ Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow ⋮ Negligibility of small divisor effects in the normal form theory for nearly-integrable Hamiltonians with decaying non-autonomous perturbations ⋮ Normal form and Nekhoroshev stability for nearly integrable Hamiltonian systems with unconditionally slow aperiodic time dependence ⋮ Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

Cites Work

• Generic Nekhoroshev theory without small divisors
• Effective stability for Gevrey and finitely differentiable prevalent Hamiltonians
• Exponential stability for time dependent potentials
• Nekhoroshev estimates for quasi-convex Hamiltonian systems
• Hamiltonian stability and subanalytic geometry
• A steepness test for analytic functions
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Complex analysis and convolution operators
• Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian
• On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
• On quantum averaging, quantum KAM, and quantum diffusion
• Unnamed Item