Asymptotics in Dynamics, Geometry and PDEs; Generalized by Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David

By Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin

Those are the complaints of a one-week foreign convention based on asymptotic research and its functions. They include significant contributions facing - mathematical physics: PT symmetry, perturbative quantum box conception, WKB research, - neighborhood dynamics: parabolic structures, small denominator questions, - new points in mildew calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, - a brand new kinfolk of resurgent features relating to knot thought.

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Extra info for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation: Proceedings of the conference held in CRM Pisa, 12-16 October 2009, Vol. I ... of the Scuola Normale Superiore / CRM Series)

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V. A RMITAGE and W. F. E BERLEIN, “Elliptic Functions”, London Mathematical Society Student Texts (No. 67), Cambridge University Press, Cambridge, 2006. Parabolic attitude Filippo Bracci Abstract. Being 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. 1 Introduction The word “dynamics” is one of the most used in mathematics. Here we use it in the sense of local discrete holomorphic dynamics, namely, the study of iterates of a germ of a holomorphic map in Cn , n ≥ 1 near a Àxed point.

85 Outer generators . . . . . . . . . . . 1 Some heuristics . . . . . . . . . 2 The short and long chains behind nur/mur . . 3 The nur transform . . . . . . . . 4 Expressing nur in terms of nir . . . . . 5 The mur transform . . . . . . . . 6 Translocation of the nur transform . . . . 7 Removal of the ingress factor . . . . . 8 Parity relations . . . . . . . . . 94 Inner generators and ordinary differential equations . . 2 ODEs for polynomial inputs f .

136 The general resurgence algebra for SP series . . . . 1 Holomorphic input f . The Àve arrows . . . 2 Meromorphic input F: the general picture . . 4 Rational inputs F: the inner algebra . . . . 150 The inner resurgence algebra for SP series . . . . 1 Polynomial inputs f . Examples . . . . . 2 Holomorphic inputs f . Examples . . . . 3 Rational inputs F. Examples . . . . . . 4 Holomorphic/meromorphic inputs F. Examples . 158 Application to some knot-related power series .

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