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L-stable Groups of Complex Diffeomorphisms with a Fixed Point.

Authors :
Martelo, M.
Scárdua, B.
Source :
Bulletin of the Brazilian Mathematical Society. Jun2018, Vol. 49 Issue 2, p463-479. 17p.
Publication Year :
2018

Abstract

We introduce a notion stability for subgroups of local complex analytic diffeomorphisms having a common fixed point, in several complex variables. This notion, called L-stability, is inspired in the notion of stability of Lyapunov for singular points and closed orbits of ordinary differential equations. It is also connected to the notion of stability for a proper leaf of a foliation in the classical sense of Reeb. We first classify in terms of the unitary group. Then we prove analytic linearization for a L-stable map and on the classification of L-stable linear groups. This is related to the study of subgroups of U(n)<inline-graphic></inline-graphic>, the unitary matrix group. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
16787544
Volume :
49
Issue :
2
Database :
Academic Search Index
Journal :
Bulletin of the Brazilian Mathematical Society
Publication Type :
Academic Journal
Accession number :
130772367
Full Text :
https://doi.org/10.1007/s00574-017-0062-8