Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms

DOI10.1016/j.physd.2008.03.047zbMath1158.37017OpenAlexW2148493717MaRDI QIDQ957606

Alejandro Luque, Jordi Villanueva

Publication date: 28 November 2008

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2008.03.047

zbMATH Keywords

numerical approximationderivatives of the rotation numberfamilies of circle maps

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical aspects of twist maps (37E40) Rotation numbers and vectors (37E45)

Related Items (12)

A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map ⋮ A numerical investigation of the pinning phenomenon in quasi-periodic Frenkel Kontorova model under an external force ⋮ A new averaging-extrapolation method for quasi-periodic frequency refinement ⋮ Rigorous enclosures of rotation numbers by interval methods ⋮ Quantitative quasiperiodicity ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations ⋮ Numerical computation of the asymptotic size of the rotation domain for the Arnold family ⋮ Effective bounds for the measure of rotations ⋮ Numerical computation of rotation numbers of quasi-periodic planar curves ⋮ Arnold maps with noise: differentiability and non-monotonicity of the rotation number ⋮ Quasi-Periodic Frequency Analysis Using Averaging-Extrapolation Methods

Uses Software

• QD

Cites Work

• Numerical computation of the asymptotic size of the rotation domain for the Arnold family
• Numerical computation of rotation numbers of quasi-periodic planar curves
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• Invariant curves of analytic perturbed nontwist area preserving maps
• Study of the transfer from the Earth to a halo orbit around the equilibrium point \(L_ 1\)
• On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
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• A structure theorem in one dimensional dynamics
• A numerical approximation of the rotation number
• On the numerical computation of Diophantine rotation numbers of analytic circle maps
• Dynamics and Mission Design Near Libration Points
• Smoothness of conjugacies of diffeomorphisms of the circle with rotations
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• Linéarisation des perturbations holomorphes des rotations et applications
• KAM theory without action-angle variables
• Generic twistless bifurcations
• Regularity of Conjugacies between Critical Circle Maps: An Experimental Study
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