Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of (c2; 0)

Tanya Firsova; Mikhail Lyubich; Remus Radu; Raluca Tanase

doi:10.24033/AST.1114

Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of (c2; 0)

Tanya Firsova
, Mikhail Lyubich
, Remus Radu
, Raluca Tanase

Mathematical Science Institute

Kansas State University
Uppsala University

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

4 Scopus citations

Abstract

Ñ We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of (C2; 0) with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of Pérez-Marco on the existence of hedgehogs for germs of univalent holomorphic maps of (C; 0) with a neutral fixed point.

Original language	English
Journal	Asterisque
Volume	416
DOIs	https://doi.org/10.24033/AST.1114
State	Published - 2020

Keywords

Brower Plane Translation Theorem
Center manifold
Hedgehogs
Holomorphic germs in C2
Invariant petals
Partial hyperbolicity

Access to Document

10.24033/AST.1114

Cite this

@article{1282b89e0d4d40dc858a7cd20cc59bd5,

title = "Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of (c2; 0)",

abstract = "{\~N} We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of (C2; 0) with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of P{\'e}rez-Marco on the existence of hedgehogs for germs of univalent holomorphic maps of (C; 0) with a neutral fixed point.",

keywords = "Brower Plane Translation Theorem, Center manifold, Hedgehogs, Holomorphic germs in C2, Invariant petals, Partial hyperbolicity",

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

year = "2020",

doi = "10.24033/AST.1114",

language = "English",

volume = "416",

journal = "Asterisque",

issn = "0303-1179",

}

TY - JOUR

T1 - Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of (c2; 0)

AU - Firsova, Tanya

AU - Lyubich, Mikhail

AU - Radu, Remus

AU - Tanase, Raluca

PY - 2020

Y1 - 2020

N2 - Ñ We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of (C2; 0) with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of Pérez-Marco on the existence of hedgehogs for germs of univalent holomorphic maps of (C; 0) with a neutral fixed point.

AB - Ñ We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of (C2; 0) with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of Pérez-Marco on the existence of hedgehogs for germs of univalent holomorphic maps of (C; 0) with a neutral fixed point.

KW - Brower Plane Translation Theorem

KW - Center manifold

KW - Hedgehogs

KW - Holomorphic germs in C2

KW - Invariant petals

KW - Partial hyperbolicity

UR - https://www.scopus.com/pages/publications/85096551197

U2 - 10.24033/AST.1114

DO - 10.24033/AST.1114

M3 - Article

AN - SCOPUS:85096551197

SN - 0303-1179

VL - 416

JO - Asterisque

JF - Asterisque

ER -

Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of (c2; 0)

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this