Numerical computation of rotation numbers of quasi-periodic planar curves

DOI10.1016/j.physd.2009.07.014zbMath1190.37048OpenAlexW2153573293MaRDI QIDQ1038452

Alejandro Luque, Jordi Villanueva

Publication date: 18 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.physd.2009.07.014

zbMATH Keywords

rotation numberinvariant curvesnumerical approximationnon-twist maps

Mathematics Subject Classification ID

Simulation of dynamical systems (37M05) Rotation numbers and vectors (37E45) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (13)

A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map ⋮ Birkhoff averages and rotational invariant circles for area-preserving maps ⋮ A new averaging-extrapolation method for quasi-periodic frequency refinement ⋮ Efficient and reliable algorithms for the computation of non-twist invariant circles ⋮ Rigorous computer-assisted application of KAM theory: a modern approach ⋮ Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average ⋮ Quantitative quasiperiodicity ⋮ Quasi-periodic orbits in Siegel disks/balls and the Babylonian problem ⋮ Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms ⋮ Effective bounds for the measure of rotations ⋮ Solving the Babylonian problem of quasiperiodic rotation rates ⋮ Birkhoff averages and the breakdown of invariant tori in volume-preserving maps ⋮ Quasi-Periodic Frequency Analysis Using Averaging-Extrapolation Methods

Uses Software

• QD

Cites Work

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