The arborification-coarborification transform: analytic, combinatorial, and algebraic aspects

DOI10.5802/afst.1083zbMath1078.37016OpenAlexW2315125958MaRDI QIDQ2484114

Bruno Vallet, Jean Écalle

Publication date: 3 August 2005

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2004_6_13_4_575_0

zbMATH Keywords

resonancesholomorphic dynamicssmall divisorsresummationnon-convergent series

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Normal forms for dynamical systems (37G05) Singularities of holomorphic vector fields and foliations (32S65) Universality and renormalization of dynamical systems (37E20) Smooth dynamical systems: general theory (37C99) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

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Cites Work

• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• Singularities that are inaccessible by geometry
• Multisummability of formal power series solutions of nonlinear meromorphic differential equations
• Correction and linearization of resonant vector fields and diffeomorphisms
• An example of local analytic \(q\)-difference equation: analytic classification
• Iteration of analytic functions
• Good uniformizing averages and an application to real resummation
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