The Fatou coordinate of a parabolic Dulac germ (CROSBI ID 698775)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Resman, Maja ; Mardešić, Pavao, Rolin, Jean-Philippe ; Županović, Vesna
engleski
The Fatou coordinate of a parabolic Dulac germ
This research is motivated by the question of cyclicity for hyperbolic polycycles in planar vector fields. We consider one-dimensional germs (at fixed point 0) which admit asymptotic expansion in power-logarithmic scale (the Dulac maps). We discuss embedding of such maps in a flow as time-one maps, that is, their rectifying Fatou coordinate. We study the transserial nature of an asymptotic expansion of the Fatou coordinate, and define an appropriate notion of integral asymptotic expansions to ensure uniqueness of the expansion. Finally, we motivate our work by fractal analysis: we answer the question of reading the formal class of a Dulac germ from the initial part of the expansion of the length of the epsilon-neighborhood of only one orbit. This is a joint work with P. Mardešić, J.P. Rolin and V. Županović.
Abel equation, Dulac germs, embeddings in a flow
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Podaci o prilogu
8-8.
2018.
objavljeno
Podaci o matičnoj publikaciji
Universality of Resurgence in Quantization Theories, http://crm.sns.it/event/433/participants.html?page=1#title
Podaci o skupu
Universality of Resurgence in Quantization Theories
pozvano predavanje
13.06.2018-15.06.2018
Pisa, Italija