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