Formal Poincaré-Dulac renormalization   for holomorphic germs

Marco Abate; Jasmin Raissy

doi:10.3934/dcds.2013.33.1773

Article Contents

2013, Volume 33, Issue 5: 1773-1807. Doi: 10.3934/dcds.2013.33.1773

This issue Previous Article Persistence of Hölder continuity for non-local integro-differential equations Next Article Gradient blow-up in Zygmund spaces for the very weak solution of a linear elliptic equation

Formal Poincaré-Dulac renormalization for holomorphic germs

Marco Abate^1, and
Jasmin Raissy^2,

1.
Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa
2.
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via Cozzi 53, 20125 Milano

Received: March 31, 2012

Revised: June 30, 2012

Published: April 2013

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Abstract

We shall describe an alternative approach to a general renormalization procedure for formal self-maps, originally suggested by Chen-Della Dora and Wang-Zheng-Peng, giving formal normal forms simpler than the classical Poincaré-Dulac normal form. As example of application we shall compute a complete list of normal forms for bi-dimensional superattracting germs with non-vanishing quadratic term; in most cases, our normal forms will be the simplest possible ones (in the sense of Wang-Zheng-Peng). We shall also discuss a few examples of renormalization of germs tangent to the identity, revealing interesting second-order resonance phenomena.

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Mathematics Subject Classification: Primary: 37G05, 37F99, 32H50.

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