Connectedness of the Arnold tongues for double standard maps

2009/04/03 by Alexandre Dezotti, Dezotti, Alexandre · 2 citations
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.0904.0593

12 pages, 4 figures, translated in english

openalex publication_date 2009/04/03 · arxiv created 2009/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We show that the Arnold tongues of the family of double standard maps f_a,b(x) = 2x + a + (b/pi) sin(2 pi x), are connected. This proof is accomplished in the complex domain by means of quasiconformal techniques and depends partly upon the fact that the complexification of f_a,b has only one critical point taking symmetry into account.

Cited by

• On the Piecewise Linear Perturbations of the Doubling Map
• Uniformization of tongues in Double Standard Map family and variation of maximal chaotic sets

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