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Download Asymptotics in Dynamics, Geometry and PDEs; Generalized by Christian Bogner, Stefan Weinzierl (auth.), Ovidiu Costin, PDF

By Christian Bogner, Stefan Weinzierl (auth.), Ovidiu Costin, Frédéric Fauvet, Frédéric Menous, David Sauzin (eds.)

These are the complaints of a one-week foreign convention situated on asymptotic research and its purposes. They comprise significant contributions facing: mathematical physics: PT symmetry, perturbative quantum box concept, WKB research, neighborhood dynamics: parabolic platforms, small denominator questions, new facets in mildew calculus, with similar combinatorial Hopf algebras and alertness to multizeta values, a brand new family members of resurgent services regarding knot theory.

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Additional resources for Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation vol. II

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1 Basic bialternals: the enumeration problem . . 2 The regular bialternals: ekma, doma . . . . 3 The irregular bialternals: carma . . . . . 4 Main differences between regular and irregular bialternals . . . . . . . . . . . 5 The pre-doma potentials . . . . . . . 6 The pre-carma potentials . . . . . . . 7 Construction of the carma bialternals . . . 9 8 9 10 11 Alternative approach . . . . . . . . The global bialternal ideal and the universal ‘restoration’ mechanism .

4 Notions of perinomal algebra . . . . . . 5 The all-encoding perinomal mould peri• . . . 6 A glimpse of perinomal splendour . . . . Provisional conclusion . . . . . . . . . 1 Arithmetical and functional dimorphy . . . 2 Moulds and bimoulds. The flexion structure . . 4 What has already been achieved . . . . . 5 Looking ahead: what is within reach and what beckons from afar . . . . . . . . Complements . . . . . . . . . . . . 1 Origin of the flexion structure .

Wr = M ... ur 1 ... 32) with a double-layered indexation wi = ( uvii ). 17), which apply in the convergent case. 36 Jean Ecalle of adding together several consecutive u i and of pairwise subtracting several vi , and that too in such a way as to conserve the scalar product du i ∧ dvi . 1 below). The flexion structure, to put it loosely but tellingly, is the sum total of all interesting operations and structures that can be constructed on BIMU by deftly combining the four elementary flexions. It turns out that these interesting structures consist, up to isomorphism, of: – seven + one Lie groups; – seven + one Lie algebras (each with its pre-Lie structure); – seven + one pre-Lie algebras.

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