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Formal classification of unfoldings of parabolic diffeomorphisms

Published online by Cambridge University Press:  01 August 2008

JAVIER RIBÓN
JAVIER RIBÓN*
Affiliation:
Departamento de Análise, Universidad Federal Fluminense, R. Mário Santos Braga, s/n, Niterói, RJ, Brasil (email: jfribon@impa.br)
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Abstract

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We provide a complete system of invariants for the formal classification of unfoldings φ(x,x1,…,xn)=(f(x,x1,…,xn),x1,…,xn) of complex analytic germs of diffeomorphisms at that are tangent to the identity. We reduce the formal classification problem to solving a linear differential equation. Then we describe the formal invariants; their nature depends on the position of the fixed points set Fix φ with respect to the regular vector field ∂/∂x. We get invariants specifically attached to higher dimension (n≥3), although generically they are analogous to the one-dimensional ones.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008 , pp. 1323 - 1365
Copyright
Copyright © 2008 Cambridge University Press

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