Titlebook: Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation; Proceedings of the c O. Costin,F. Fauvet,D. Sauzin Conference proc

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Expanding a Function in an Orthogonal BasisBeing parabolic in complex dynamics is not a state of fact, but it is more an attitude. In these notes we explain the philosophy under this assertion.

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https://doi.org/10.1007/978-3-0348-7448-9We present a new proof, under a slightly different (and more natural) arithmetic hypothesis, and using direct computations via power series expansions, of a holomorphic linearization result in presence of resonances originally proved by Rüssmann.

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Brjuno conditions for linearization in presence of resonances,We present a new proof, under a slightly different (and more natural) arithmetic hypothesis, and using direct computations via power series expansions, of a holomorphic linearization result in presence of resonances originally proved by Rüssmann.

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Noncommutative symmetric functions and combinatorial Hopf algebras,ular, some of these algebras have connections with mould calculus and resurgence theory. They can be approached in many different ways. Here, they will be regarded as generalizations of the algebra of symmetric functions.

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Conference proceedings 2011s dealing with- mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis,- local dynamics: parabolic systems, small denominator questions, - new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values,- a new family of resurgent functions related to knot theory.

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