Numerical determination of the continued fraction expansion of the rotation number

DOI10.1016/0167-2789(92)90211-5zbMath0761.58036OpenAlexW1965156150WikidataQ59184919 ScholiaQ59184919MaRDI QIDQ1207223

Henk Bruin

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90211-5

zbMATH Keywords

algorithmrotation numbercontinued fraction expansionhomeomorphisms on the circle

Mathematics Subject Classification ID

Topological dynamics (37B99) Continued fractions and generalizations (11J70) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (8)

The numerical approximation of the rotation number of planar maps ⋮ Rigorous enclosures of rotation numbers by interval methods ⋮ Delayed feedback control and phase reduction of unstable quasi-periodic orbits ⋮ Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms ⋮ On the numerical computation of Diophantine rotation numbers of analytic circle maps ⋮ Effective bounds for the measure of rotations ⋮ Numerical computation of rotation numbers of quasi-periodic planar curves ⋮ Stabilization Control of Quasi-periodic Orbits

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Functional equations for circle homeomorphisms with golden ratio rotation number
• A new proof of M. Herman's theorem
• On the numerical approximation of the rotation number
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
• Smooth conjugacy and renormalisation for diffeomorphisms of the circle

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