Search results for " 30B10"

showing 2 items of 2 documents

Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets

2006

We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.

Power seriesDiscrete mathematics28A80Social connectednessGeneral Mathematics010102 general mathematics01 natural sciencesSet (abstract data type)Bernoulli's principleFractal30C1528A80 30B10Mathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematicsself-affine fractals010307 mathematical physicsAffine transformationZeros of power series0101 mathematicsMathematics
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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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