6533b860fe1ef96bd12c3a71

RESEARCH PRODUCT

Normal forms and embeddings for power-log transseries

Jean-philippe RolinMaja ResmanPavao MardešićVesna ŽUpanović

subject

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 theory

description

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 Županović.

yearjournalcountryeditionlanguage
2016-11-05Advances in Mathematics
https://doi.org/10.1016/j.aim.2016.08.030