Normal forms and embeddings for power-log transseries

Normal forms and embeddings for power-log transseries

Dulac series are asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras of power-log transseries (generalized series) which extend the algebra of Dulac series. We give a formal normal form and prove a formal embedding theorem...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2016-11, Vol.303, p.888-953
Hauptverfasser: Mardešić, P., Resman, M., Rolin, J.-P., Županović, V.
Format: Artikel
Sprache:eng
Schlagworte:
Classical Analysis and ODEs
Dulac map
Dynamical Systems
Embedding in a flow
Iteration theory
Mathematics
Normal forms
Transseries
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Beschreibung
Zusammenfassung:Dulac series are asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras of power-log transseries (generalized series) which extend the algebra of Dulac series. We give a formal normal form and prove a formal embedding theorem for transseries in these algebras.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.08.030