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RESEARCH PRODUCT

Normal forms of hyperbolic logarithmic transseries

D. PeranM. ResmanJ.p. RolinT. Servi

subject

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 12J15Analysis

description

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.

yearjournalcountryeditionlanguage
2021-06-17Journal of Differential Equations
https://doi.org/10.1016/j.jde.2022.12.002