Regularity of Conjugacies between Critical Circle Maps: An Experimental Study

DOI10.1080/10586458.2002.10504688zbMath1116.37306OpenAlexW1965725659MaRDI QIDQ5472020

Rafael de la Llave, Nikola P. Petrov

Publication date: 14 June 2006

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1062621217

zbMATH Keywords

self-similarityrenormalizationCritical circle mapssmoothness of conjugacies

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Abstract harmonic analysis (43A99) Universality and renormalization of dynamical systems (37E20) Approximation methods and numerical treatment of dynamical systems (37M99) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04)

Related Items (14)

Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map ⋮ 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 ⋮ Breakup of shearless meanders and “outer” tori in the standard nontwist map ⋮ The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture ⋮ Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms ⋮ Numerical Computation of Periodic Orbits and Isochrons for State-Dependent Delay Perturbation of an ODE in the Plane ⋮ A numerical estimate of the regularity of a family of strange non-chaotic attractors ⋮ On the numerical computation of Diophantine rotation numbers of analytic circle maps ⋮ Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall ⋮ Numerical computation of rotation numbers of quasi-periodic planar curves ⋮ Regularization of Brouwer translation theorem ⋮ Boundaries of Siegel disks: Numerical studies of their dynamics and regularity ⋮ Breakdown of invariant attractors for the dissipative standard map

Uses Software

• doubledouble

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