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Formal classification of unfoldings of parabolic diffeomorphisms
Published online by Cambridge University Press: 01 August 2008
Abstract
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.
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- Copyright © 2008 Cambridge University Press
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