0000000000415440

AUTHOR

T. Servi

showing 2 related works from this author

Normal forms of hyperbolic logarithmic transseries

2021

We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.

Applied MathematicsMathematics::History and OverviewFOS: Mathematicsfixed point theory ; formal normal forms ; hyperbolic fixed point ; Koenigs sequence ; linearization ; logarithmic transseries[MATH] Mathematics [math]Dynamical Systems (math.DS)Mathematics - Dynamical Systems[MATH]Mathematics [math]34C20 37C25 47H10 39B12 46A19 26A12 12J15AnalysisJournal of Differential Equations
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Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras

2013

International audience; An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.

Pure mathematics30D60 14P15 03C64 (primary) 32S45 (secondary)Mathematics::Complex VariablesGeneral Mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics::Classical Analysis and ODEso-minimality16. Peace & justice[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic Geometryquantifier eliminationQuantifier eliminationquasianalyticityFOS: Mathematics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG][MATH]Mathematics [math]rectilinearisationAlgebraic Geometry (math.AG)Mathematics
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