Sur les dynamiques holomorphes non linéarisables et une conjecture de V. I. Arnold

DOI10.24033/asens.1681zbMath0812.58051OpenAlexW2475072017WikidataQ123344857 ScholiaQ123344857MaRDI QIDQ4289249

Ricardo Pérez-Marco

Publication date: 24 May 1994

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1993_4_26_5_565_0

zbMATH Keywords

periodic pointscircle diffeomorphismsArnolds conjecturenon-linearizable holomorphic germs

Mathematics Subject Classification ID

Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Iteration of real functions in one variable (26A18)

Related Items (23)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extending holomorphic motions
• Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
• Über die Häufigkeit der Nichtzentren
• Iteration of analytic functions
• On the dynamics of rational maps
• On the dynamics of polynomial-like mappings
• A note on non-linearizable analitic functions
• Differential Topology
• Small denominators. I. Mappings of the circumference onto itself

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