engleski

Epsilon-neighborhoods of orbits of parabolic germs and cohomological equations

We consider germs of parabolic diffeomorphisms f : (C ; 0) -> (C ; 0) with the multiplier equal to 1. The question is if we can recognize a germ using the (directed) areas of epsilon-neighborhoods of discrete orbits. We have shown that the formal class can be read from finitely many terms in the asymptotic expansion in epsilon for any orbit. In this talk, we discuss analyticity properties of functions of (directed) areas of epsilon-neighborhoods of orbits. 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 difference equation similar to the trivialisation equation.

parabolic germs; epsilon-neighborhoods; cohomological equations

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