6533b831fe1ef96bd1299874

RESEARCH PRODUCT

The Fatou coordinate for parabolic Dulac germs

Vesna ŽUpanovićMaja ResmanPavao MardešićJean-philippe Rolin

subject

Pure mathematicsMonomialClass (set theory)Mathematics::Dynamical SystemsConstructive proofLogarithmTransseries[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]orbitsDulac germAsymptotic expansionDynamical Systems (math.DS)01 natural sciencesMSC: 37C05 34C07 30B10 30B12 39A06 34E05 37C10 37C1537C05 34C07 30B10 30B12 39A06 34E05 37C10 37C15Mathematics::Algebraic GeometryFOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsMathematicsDulac germ ; Fatou coordinate ; Embedding in a flow ; Asymptotic expansion ; TransseriesdiffeomorphismsMathematics::Complex VariablesApplied Mathematics010102 general mathematicsFatou coordinate010101 applied mathematicsclassificationnormal formsepsilon-neighborhoodsEmbedding in a flowAsymptotic expansionAnalysis

description

We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.

yearjournalcountryeditionlanguage
2017-10-02
10.1016/j.jde.2018.09.008https://doi.org/10.1016/j.jde.2018.09.008