0000000000053596

AUTHOR

Tamara Servi

showing 2 related works from this author

Multisummability for generalized power series

2022

We develop multisummability, in the positive real direction, for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all multisums of these series. This resulting structure expands both $\mathbb{R}_{\mathcal{G}}$ and the reduct of $\mathbb{R}_{\mathrm{an}^*}$ generated by all convergent generalized power series with natural support; in particular, its expansion by the exponential function defines both the Gamma function on $(0,\infty)$ and the Zeta function on $(1,\infty)$.

Mathematics - Classical Analysis and ODEsGeneral MathematicsClassical Analysis and ODEs (math.CA)FOS: Mathematics[MATH] Mathematics [math]Mathematics - LogicLogic (math.LO)Primary 40C10 03C64 26E10 Secondary 30D60
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Linearization of complex hyperbolic Dulac germs

2021

We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.

Pure mathematicsMathematics::Dynamical SystemsMathematics::Complex VariablesApplied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsDynamical Systems (math.DS)01 natural sciencesDomain (mathematical analysis)Dulac germs and series ; Hyperbolic fixed point ; Linearization ; Koenigs' sequenceQuadratic equationLinearization0103 physical sciencesFOS: MathematicsGerm010307 mathematical physics0101 mathematicsMathematics - Dynamical SystemsAnalysisMathematics
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