Effective bounds for the measure of rotations
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Publication:5207515
DOI10.1088/1361-6544/ab500dzbMath1436.37052arXiv1806.05517OpenAlexW2995487166MaRDI QIDQ5207515
Jordi-Lluís Figueras, Àlex Haro, Alejandro Luque
Publication date: 2 January 2020
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.05517
Dynamical systems involving maps of the circle (37E10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Rotation numbers and vectors (37E45)
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- The parameterization method for invariant manifolds. From rigorous results to effective computations
- Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations
- The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
- Computation of whiskered invariant tori and their associated manifolds: new fast algorithms
- A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results
- On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems
- Stability islands in the vicinity of separatrices of near-integrable symplectic maps
- Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms
- Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions
- Herman's theory revisited
- Numerical computation of rotation numbers of quasi-periodic planar curves
- Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
- A new proof of M. Herman's theorem
- Construction of analytic KAM-surfaces and effective stability bounds
- Some open problems in dynamical systems
- Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
- The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
- Numerical determination of the continued fraction expansion of the rotation number
- On the stability of realistic three-body problems
- A-posteriori KAM theory with optimal estimates for partially integrable systems
- Rigorous computer-assisted application of KAM theory: a modern approach
- Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown
- Computation of quasiperiodic normally hyperbolic invariant tori: rigorous results
- A numerical approximation of the rotation number
- Existence of knotted vortex tubes in steady Euler flows
- Around the stability of KAM tori
- A KAM theory for conformally symplectic systems: efficient algorithms and their validation
- Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
- On the numerical computation of Diophantine rotation numbers of analytic circle maps
- Reliable Computation of Robust Response Tori on the Verge of Breakdown
- Lagrangian tori near resonances of near-integrable Hamiltonian systems
- Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map
- A KAM theorem without action-angle variables for elliptic lower dimensional tori
- On the stability of mechanical systems
- Integrability of hamiltonian systems on cantor sets
- KAM stability and celestial mechanics
- Smoothness of conjugacies of diffeomorphisms of the circle with rotations
- Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps
- Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
- Generalized implicit function theorems with applications to some small divisor problems, I
- On optimal estimates for the solutions of linear difference equations on the circle
- Quantitative quasiperiodicity
- KAM theory without action-angle variables
- Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
- PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
- The KAM Story
- Invariant tori in the secular motions of the three-body planetary systems
