engleski

Epsilon-neighborhoods of orbits and classifications of parabolic germs

We consider analytic germs of diffeomorphisms f:(C, 0)->(C, 0) tangent to the identity, called parabolic germs. In this talk, we disuss the question of recognizing a germ using the functions of the (directed) areas of the epsilon- neighborhoods of its orbits. We have shown that the formal class can be read from finitely many terms in the asymptotic expansion of this area function in epsilon. We further discuss the analyticity properties of this function. In particular, we concentrate on the coefficient of the quadratic term in the expansion, as a function of the initial point. It satisfies a cohomological equation similar to the trivialisation equation.

parabolic diffeomorphisms; epsilon-neighborhoods; formal and analytic classification

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