Search results for "Embedding in a flow"

showing 2 items of 2 documents

Normal forms and embeddings for power-log transseries

2016

First return maps in the neighborhood of hyperbolic polycycles have their asymptotic expansion as Dulac series, which are series with power-logarithm monomials. We extend the class of Dulac series to an algebra of power-logarithm transseries. Inside this new algebra, we provide formal normal forms of power-log transseries and a formal embedding theorem. The questions of classifications and of embeddings of germs into flows of vector fields are common problems in dynamical systems. Aside from that, our motivation for this work comes from fractal analysis of orbits of first return maps around hyperbolic polycycles. This is a joint work with Pavao Mardešić, Jean-Philippe Rolin and Vesna Župano…

Mathematics::Dynamical Systems[ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA]TransseriesGeneral Mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]MSC: 34C20 37C10 39B12 46A19 28A75 58K50 26A12[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]Normal forms01 natural sciencesIteration theory ; Dulac map ; normal forms ; embedding in a flow ; transseries.0101 mathematicsAlgebra over a fieldMathematicsSeries (mathematics)Dulac mapIteration theoryformal normal forms parabolic transseriesMathematics::History and Overview010102 general mathematicsPower (physics)010101 applied mathematicsAlgebraEmbeddingEmbedding in a flowIteration theoryAdvances in Mathematics
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The Fatou coordinate for parabolic Dulac germs

2017

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.

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
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