An implosion arising from saddle connection in 2D complex dynamics

DOI10.1512/iumj.2019.68.7577zbMath1422.32023OpenAlexW2920117092WikidataQ128279915 ScholiaQ128279915MaRDI QIDQ5225148

Shizuo Nakane, Hiroyuki Inou

Publication date: 19 July 2019

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/407cd3bee7b77660f00b6420dc974ccfbb496c85

zbMATH Keywords

saddle connectionimplosionLavaurs mapfiber Julia-Lavaurs set

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (2)

On formal normal forms of holomorphic germs at super-saddle fixed points ⋮ Fiber Julia sets of polynomial skew products with super-saddle fixed points

Cites Work

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• The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
• Dynamics of polynomial skew products on \(\mathbb{C}^2\)
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• A dichotomy for Fatou components of polynomial skew products
• Continuity of fiber Julia sets for Axiom A polynomial skew products on ‒²
• Axiom A polynomial skew products of 2 and their postcritical sets
• Tessellation and Lyubich–Minsky laminations associated with quadratic maps, I: pinching semiconjugacies
• Discrete holomorphic local dynamical systems
• Dynamics in One Complex Variable. (AM-160)

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