engleski

Classifications of parabolic germs and epsilon-neighborhoods of orbits

We consider analytic germs of parabolic diffeomorphisms f:C->C. The question is if we could recognize a germ using the functions of the (directed) areas of the epsilon-neighborhoods of its orbits. We show that the formal class can be read from only finitely many terms in the asymptotic expansion of the (directed) area function in epsilon. We further discuss analytic properties of this function. 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

epsilon-neighborhoods; parabolic germs; classifications

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