Hedgehogs in higher dimensions and their applications

Mikhail Lyubich; Remus Radu; Raluca Tanase

doi:10.24033/AST.1115

Hedgehogs in higher dimensions and their applications

Mikhail Lyubich
, Remus Radu
, Raluca Tanase

Mathematical Science Institute

Uppsala University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper we study the dynamics of germs of holomorphic diffeomorphisms of (Cⁿ, 0) with a fixed point at the origin with exactly one neutral eigenvalue. We prove that the map on any local center manifold of 0 is quasiconformally conjugate to a holomorphic map and use this to transport results from one complex dimension to higher dimensions.

Original language	English
Pages (from-to)	213-251
Number of pages	39
Journal	Asterisque
Volume	416
DOIs	https://doi.org/10.24033/AST.1115
State	Published - 2020

Keywords

Center manifold
Fatou coordinates
Hedgehogs
Holomorphic germs in C
Measurable Riemann Mapping Theorem
Partial hyperbolicity

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10.24033/AST.1115

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title = "Hedgehogs in higher dimensions and their applications",

abstract = "In this paper we study the dynamics of germs of holomorphic diffeomorphisms of (Cn, 0) with a fixed point at the origin with exactly one neutral eigenvalue. We prove that the map on any local center manifold of 0 is quasiconformally conjugate to a holomorphic map and use this to transport results from one complex dimension to higher dimensions.",

keywords = "Center manifold, Fatou coordinates, Hedgehogs, Holomorphic germs in C, Measurable Riemann Mapping Theorem, Partial hyperbolicity",

author = "Mikhail Lyubich and Remus Radu and Raluca Tanase",

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T1 - Hedgehogs in higher dimensions and their applications

AU - Lyubich, Mikhail

AU - Radu, Remus

AU - Tanase, Raluca

N1 - Publisher Copyright: © Astérisque 416, SMF 2020

PY - 2020

Y1 - 2020

N2 - In this paper we study the dynamics of germs of holomorphic diffeomorphisms of (Cn, 0) with a fixed point at the origin with exactly one neutral eigenvalue. We prove that the map on any local center manifold of 0 is quasiconformally conjugate to a holomorphic map and use this to transport results from one complex dimension to higher dimensions.

AB - In this paper we study the dynamics of germs of holomorphic diffeomorphisms of (Cn, 0) with a fixed point at the origin with exactly one neutral eigenvalue. We prove that the map on any local center manifold of 0 is quasiconformally conjugate to a holomorphic map and use this to transport results from one complex dimension to higher dimensions.

KW - Center manifold

KW - Fatou coordinates

KW - Hedgehogs

KW - Holomorphic germs in C

KW - Measurable Riemann Mapping Theorem

KW - Partial hyperbolicity

UR - https://www.scopus.com/pages/publications/85096530590

U2 - 10.24033/AST.1115

DO - 10.24033/AST.1115

M3 - Article

AN - SCOPUS:85096530590

SN - 0303-1179

VL - 416

SP - 213

EP - 251

JO - Asterisque

JF - Asterisque

ER -

Hedgehogs in higher dimensions and their applications

Abstract

Keywords

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