Analytic smoothing of geometric maps with applications to KAM theory

DOI10.1016/j.jde.2008.05.009zbMath1160.37024OpenAlexW2015592938MaRDI QIDQ942184

A. González-Enríquez, Rafael de la Llave

Publication date: 4 September 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.05.009

zbMATH Keywords

smoothinguniquenessapproximationKAM torisymplectic mapscontact mapsbootstrap of regularityvolume-preserving maps

Mathematics Subject Classification ID

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

Related Items

Existence of knotted vortex structures in stationary solutions of the Euler equations ⋮ Beltrami fields exhibit knots and chaos almost surely ⋮ An estimate of smoothing and composition with applications to conjugation problems ⋮ A KAM theory for conformally symplectic systems: efficient algorithms and their validation ⋮ Existence of invariant tori for differentiable Hamiltonian vector fields without action-angle variables ⋮ A new approach to the parameterization method for Lagrangian tori of Hamiltonian systems ⋮ A Parameterization Method for Lagrangian Tori of Exact Symplectic Maps of $R^2r$ ⋮ Existence of whiskered KAM tori of conformally symplectic systems ⋮ Phase transitions on the Markov and Lagrange dynamical spectra ⋮ Unnamed Item ⋮ Existence of knotted vortex tubes in steady Euler flows

Cites Work

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• On a partial differential equation involving the Jacobian determinant
• Lipschitz spaces, smoothness of functions, and approximation theory
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Regularity of the composition operator in spaces of Hölder functions
• KAM theory in configuration space
• Formes-volume sur les variétés à bord
• An estimate of smoothing and composition with applications to conjugation problems
• Implicit function theorems and isometric embeddings
• A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
• Diffeomorphisms and Volume-Preserving Embeddings of Noncompact Manifolds
• Generalized implicit function theorems with applications to some small divisor problems, I
• Note on sums containing small divisors
• On optimal estimates for the solutions of linear difference equations on the circle
• KAM theory without action-angle variables
• A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
• On the Volume Elements on a Manifold