Hölder continuity property of filled-in Julia sets in $\mathbb \{C\}^n$

DOI10.1090/S0002-9939-97-03808-2zbMath0865.31006WikidataQ120835883 ScholiaQ120835883MaRDI QIDQ4339180

Marta Kosek

Publication date: 5 June 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Julia setMarkov's inequalitypluricomplex Green function

Mathematics Subject Classification ID

Pluriharmonic and plurisubharmonic functions (31C10) Plurisubharmonic functions and generalizations (32U05)

Related Items (14)

Stability and bifurcations in projective holomorphic dynamics ⋮ Complete invariance and compactness of the filled Julia sets of polynomial maps in \( \mathbb {C}^N \) ⋮ Markov-Type Inequalities with Applications in Multivariate Approximation Theory ⋮ Iterated function systems and Łojasiewicz-Siciak condition of Green's function ⋮ Equilibrium states of endomorphisms of \(\mathbb{P}^k\). I: Existence and properties ⋮ Strong analyticity of partly filled-in composite Julia sets ⋮ The Łojasiewicz-Siciak condition of the pluricomplex Green function ⋮ Composite Julia sets generated by infinite polynomial arrays. ⋮ Hölder continuity of the Green function and Markov brothers' inequality ⋮ Iteration of Analytic Multifunctions ⋮ Markov inequality in several variables ⋮ ŁS condition for filled Julia sets in \(\mathbb {C}\) ⋮ Approximation of holomorphic functions on compact subsets of \(\mathbb R^N\) ⋮ Regularity of dynamical Green’s functions

Cites Work

• Markov's inequality and \(C^{\infty}\) functions on sets with polynomial cusps
• Complex Hénon mappings in \({\mathbb{C}}^ 2\) and Fatou-Bieberbach domains
• Complex dynamics
• Extremal plurisubharmonic functions in $C^N$
• Metrics Associated with Extremal Plurisubharmonic Functions
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