Parabolic Bifurcations in Complex Dimension 2

2012/08/13 by Eric Bedford, Bedford, Eric, John Smillie +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1208.2577

openalex publication_date 2012/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider parabolic bifurcations of families of diffeomorphisms in two complex dimensions. Specifically we consider a two variable family of diffeomorphisms F_ε: M→ M given locally by F_ε(x,y) = (x + x² + ε²+ ..., b_εy+...) where |b_ε|<1, and the `...' terms involve x, y and ε.

Cited by

• Normal forms and Misiurewicz renormalization for dissipative surface diffeomorphisms
• Semi-parabolic tools for hyperbolic Hénon maps and continuity of Julia sets in ℂ²

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