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Documents  Sauzin, David | enregistrements trouvés : 4

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Research talks;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry

Ecalle’s resurgent functions appear naturally as Borel transforms of divergent series like Stirling series, formal solutions of differential equations like Euler series, or formal series associated with many other problems in Analysis and dynamical systems. Resurgence means a certain property of analytic continuation in the Borel plane, whose stability under con- volution (the Borel counterpart of multiplication of formal series) is not obvious. Following the analytic continuation of the convolution of several resurgent functions is indeed a delicate question, but this must be done in an explicit quan- titative way so as to make possible nonlinear resurgent calculus (e.g. to check that resurgent functions are stable under composition or under substitution into a convergent series). This can be done by representing the analytic continuation of the convolution product as the integral of a holomorphic n-form on a singular n-simplex obtained as a suitable explicit deformation of the standard n-simplex. The theory of currents is convenient to deal with such integrals of holomorphic forms, because it allows to content oneself with little regularity: the deformations we use are only Lipschitz continuous, because they are built from the flow of non-autonomous Lipschitz vector fields. Ecalle’s resurgent functions appear naturally as Borel transforms of divergent series like Stirling series, formal solutions of differential equations like Euler series, or formal series associated with many other problems in Analysis and dynamical systems. Resurgence means a certain property of analytic continuation in the Borel plane, whose stability under con- volution (the Borel counterpart of multiplication of formal series) is not obvious. ...

30D05 ; 37FXX

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- 145 p.
ISBN 978-0-8218-3268-4

Memoirs of the american mathematical society , 0775

Localisation : Collection 1er étage

système hamiltonien # variété invariante # géométrie symplectique # découpage des variétés invariantes # diffusion de Arnold # théorème de Nekhoroshev # système presque intégrable

70H08 ; 70H09 ; 35J40 ; 37D10 ; 34C37

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- 83 p.
ISBN 978-0-8218-3325-4

Memoirs of the american mathematical society , 0780

Localisation : Collection 1er étage

fonction monogène # petit diviseur # fonction quasianalytique # fraction continue # classe de Carleman # résurgence # produit d'Hadamard

37F50 ; 30D60 ; 30G30 ; 11A55 ; 11J06 ; 40G10 ; 34M37

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- vi; 110 p.
ISBN 978-1-4704-3492-2

Memoirs of the American Mathematical Society , 1235

Localisation : Collection 1er étage

difféomorphisme # difféomorphisme intégrable # domaine d'errance # théorie de Nakhoroshev # diffusion d'Arnold # perturbation hamiltonienne # système de Gevrey quasi-intégrable

53D22 ; 70H08 ; 26E10

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