Length of epsilon-neighborhoods of orbits of Dulac maps
| Autor: | Mardesic, P., Resman, M., Rolin, J. -P., Zupanovic, V. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | By Dulac maps we mean first return maps of hyperbolic polycycles of analytic planar vector fields. We study the fractal properties of the orbits of a parabolic Dulac map. To this end, we prove that it admits a Fatou coordinate with an asympotic expansion in terms of power-iterated logarithm transseries. This allows to introduce a new notion, the \emph{continuous time length of $\varepsilon$-neighborhoods of orbits}, and to prove that this function of $\varepsilon$ admits an asymptotic expansion in the same scale. We show that, under some hypotheses, this expansion determines the class of formal conjugacy of the Dulac map. Comment: 43 pages, 1 figure |
| Databáze: | arXiv |
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