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Analytic invariants associated with a parabolic fixed point in C2

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Gelfreich, Vassili and Naudot, V.. (2008) Analytic invariants associated with a parabolic fixed point in C2. Ergodic Theory and Dynamical Systems, Vol.28 (No.6). pp. 1815-1848. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385707001046

Abstract

It is well known that in a small neighbourhood of a parabolic fixed point a real-analytic diffeomorphism of (R2,0) embeds in a smooth autonomous flow. In this paper we show that the complex-analytic situation is completely different and a generic diffeomorphism cannot be embedded in an analytic flow in a neighbourhood of its parabolic fixed point. We study two analytic invariants with respect to local analytic changes of coordinates. One of the invariants was introduced earlier by one of the authors. These invariants vanish for time-one maps of analytic flows. We show that one of the invariants does not vanish on an open dense subset. A complete analytic classification of the maps with a parabolic fixed point in C2 is not available at the present time.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Parabolic operators, Diffeomorphisms, Invariants, Mappings (Mathematics), Differential topology
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	December 2008
Volume:	Vol.28
Number:	No.6
Page Range:	pp. 1815-1848
Identification Number:	10.1017/S0143385707001046
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/C000595/1 (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/860