Hamiltonian perturbation theory for ultra-differentiable functions

DOI10.1090/memo/1319zbMath1487.37001arXiv1710.01156OpenAlexW2762553802MaRDI QIDQ3380551

Jacques Féjoz, Abed Bounemoura

Publication date: 29 September 2021

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.01156

zbMATH Keywords

KAM theoryArnold diffusionNekhoroshev theoryultra-differentiable functions

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Related Items

Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications ⋮ A \(C^\infty\) Nekhoroshev theorem ⋮ Optimal linearization of vector fields on the torus in non-analytic Gevrey classes ⋮ Response solutions for quasi-periodically forced harmonic oscillators in Gevrey class ⋮ Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications ⋮ Analytic smoothing and Nekhoroshev estimates for Hölder steep Hamiltonians ⋮ Linearization of ultra-differentiable circle flows beyond Brjuno condition

Cites Work

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• The steep Nekhoroshev's theorem
• Normal forms, stability and splitting of invariant manifolds. I: Gevrey Hamiltonians
• Optimal stability and instability for near-linear Hamiltonians
• Generic Nekhoroshev theory without small divisors
• Superexponential stability of quasi-periodic motion in Hamiltonian systems
• Effective stability for Gevrey and finitely differentiable prevalent Hamiltonians
• Speed of Arnold diffusion for analytic Hamiltonian systems
• Kolmogorov theorem revisited
• The implicit function theorem for ultradifferentiable mappings
• Ultradifferentiability of solutions of ordinary differential equations
• Lie series method for vector fields and Hamiltonian perturbation theory
• Surjectivity of the restriction map to a compact in classes of ultradifferentiable functions
• Nekhoroshev estimates for quasi-convex Hamiltonian systems
• The Lagrange inversion formula on non-Archimedean fields. Non-analytical form of differential and finite difference equations
• Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
• Division by flat ultradifferentiable functions and sectorial extensions
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Local rigidity of Diophantine translations in higher-dimensional tori
• Destruction of Lagrangian torus for positive definite Hamiltonian systems
• A Diophantine duality applied to the KAM and Nekhoroshev theorems
• On quasianalytic local rings
• The classical KAM theorem for Hamiltonian systems via rational approximations
• Improved exponential stability for near-integrable quasi-convex Hamiltonians
• Introduction to the Perturbation Theory of Hamiltonian Systems
• KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition
• Arnold's example with three rotators
• Complex analysis and convolution operators
• Gevrey separation of fast and slow variables
• Gevrey and Analytic Convergence of Picard'S Successive Approximations
• An analytic counterexample to the KAM theorem
• Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb C},0)$
• Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian
• Weak mixing for reparameterized linear flows on the torus
• An approach to arnold's diffusion through the calculus of variations
• Improved stability for analytic quasi-convex nearly integrable systems and optimal speed of Arnold diffusion
• KAM theorem for Gevrey Hamiltonians
• Nonlinear hyperbolic equations