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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Partially hyperbolic fixed
points with constraints

Author: Patrick Bonckaert
Journal: Trans. Amer. Math. Soc. 348 (1996), 997-1011
MSC (1991): Primary 58F14, 58F36, 34C20
MathSciNet review: 1321568
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Abstract: We investigate the local conjugacy, at a partially hyperbolic fixed point, of a diffeomorphism (vector field) to its normally linear part in the presence of constraints, where the change of variables also must satisfy the constraints. The main result is applied to vector fields respecting a singular foliation, encountered, by F. Dumortier and R. Roussarie, in the desingularization of families of vector fields.

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Additional Information

Patrick Bonckaert
Affiliation: Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium

Keywords: Partially hyperbolic fixed point, normal form, constraint, structure preserving
Received by editor(s): March 8, 1994
Article copyright: © Copyright 1996 American Mathematical Society