Sauzin, D. 1966
Overview
Works:  29 works in 90 publications in 3 languages and 1,242 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Other, Author, Opponent, 958 
Classifications:  QA3, 515.354 
Publication Timeline
.
Most widely held works by
D Sauzin
Divergent series, summability and resurgence by
Claude Mitschi(
)
14 editions published in 2016 in English and German and held by 288 WorldCat member libraries worldwide
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The RiemannHilbert problem is discussed from Bolibrukh's point of view. The second part expounds 1summability and Ecalle's theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via zalien calculusy, which provides a full description of the Stokes phenomenon for linear or nonlinear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra
14 editions published in 2016 in English and German and held by 288 WorldCat member libraries worldwide
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The RiemannHilbert problem is discussed from Bolibrukh's point of view. The second part expounds 1summability and Ecalle's theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via zalien calculusy, which provides a full description of the Stokes phenomenon for linear or nonlinear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra
Quasianalytic monogenic solutions of a cohomological equation by
S Marmi(
Book
)
11 editions published between 2001 and 2003 in English and held by 263 WorldCat member libraries worldwide
Introduction Monogenic properties of the solutions of the cohomological equation Carleman classes at diophantine points Resummation at resonances and constanttype points Conclusions and applications Appendix Bibliography
11 editions published between 2001 and 2003 in English and held by 263 WorldCat member libraries worldwide
Introduction Monogenic properties of the solutions of the cohomological equation Carleman classes at diophantine points Resummation at resonances and constanttype points Conclusions and applications Appendix Bibliography
On the splitting of invariant manifolds in multidimensional nearintegrable Hamiltonian systems by
Pierre Lochak(
Book
)
8 editions published in 2003 in English and held by 253 WorldCat member libraries worldwide
8 editions published in 2003 in English and held by 253 WorldCat member libraries worldwide
Resurgence, physics and numbers by Physics and Numbers Conference Resurgence(
)
10 editions published in 2017 in English and held by 215 WorldCat member libraries worldwide
This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 1822, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years  a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. .
10 editions published in 2017 in English and held by 215 WorldCat member libraries worldwide
This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 1822, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years  a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. .
Asymptotics in dynamics, geometry and PDEs : generalized Borel summation by
Ovidiu Costin(
)
8 editions published in 2011 in English and held by 67 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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, and a new family of resurgent functions related to knot theory
8 editions published in 2011 in English and held by 67 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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, and a new family of resurgent functions related to knot theory
Asymptotics in Dynamics, Geometry and PDEs ; Generalized Borel Summation vol. I by
O Costin(
)
8 editions published in 2011 in English and held by 34 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
8 editions published in 2011 in English and held by 34 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
Divergent series, summability and resurgence(
Book
)
3 editions published in 2016 in English and held by 24 WorldCat member libraries worldwide
3 editions published in 2016 in English and held by 24 WorldCat member libraries worldwide
Asymptotics in Dynamics, Geometry and PDEs ; Generalized Borel Summation vol. II by
Ovidiu Costin(
)
3 editions published in 2011 in English and held by 22 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
3 editions published in 2011 in English and held by 22 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
Monodromy and Resurgence by
Claude Mitschi(
)
3 editions published in 2016 in English and held by 19 WorldCat member libraries worldwide
3 editions published in 2016 in English and held by 19 WorldCat member libraries worldwide
Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation vol. II by
Ovidiu Costin(
)
1 edition published in 2011 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 18 WorldCat member libraries worldwide
On the splitting of invariant manifolds in multidimensional nearintegrable Hamiltonian systems by
Pierre Lochak(
Book
)
1 edition published in 2003 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 14 WorldCat member libraries worldwide
Measure and capacity of wandering domains in Gevrey nearintegrable exact symplectic systems by
Laurent Lazzarini(
)
2 editions published in 2019 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 2019 in English and held by 13 WorldCat member libraries worldwide
Asymptotics in dynamics, geometry and PDEs; generalized Borel summation(
)
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
Asymptotics in dynamics, geometry and PDEs; generalized Borel summation(
)
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
These are the proceedings of a oneweek international conference centered on asymptotic analysis and its applications. They contain major contributions 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
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé by
David Sauzin(
Book
)
2 editions published in 1994 in French and held by 5 WorldCat member libraries worldwide
La théorie et les méthodes développées par Jean Ecalle sous le nom de fonctions résurgentes sont appliquées au problème de la séparation des variétés stable et instable d'un pendule perturbé ; ce problème a été posé par Henri Poincaré dans les méthodes nouvelles de la mécanique céleste. Le système dynamique en question est un système hamitonien, avec un terme perturbatif dont la période est un petit paramètre singulier et dont la taille est mesurée par un paramètre auxiliaire non singulier. (l'étude complète n'est menee à bien qu'au prix d'une simplification de ce terme). Comme Poincaré, nous décrivons les variétés stables et instables à l'aide de deux solutions de l'équation de HamiltonJacobi, trouvées en effectuant des développements convergents en puissances du paramètre non singulier. Ces solutions admettent le même développement asymptotique divergent par rapport au paramètre singulier, la divergence étant de type résurgent. Ceci permet de mesurer leur écart par la dérivation étrangère dont l'indice est le point singulier le plus proche de l'origine : on trouve un équivalent asymptotique exponentiellement petit par rapport au paramètre de perturbation singulière
2 editions published in 1994 in French and held by 5 WorldCat member libraries worldwide
La théorie et les méthodes développées par Jean Ecalle sous le nom de fonctions résurgentes sont appliquées au problème de la séparation des variétés stable et instable d'un pendule perturbé ; ce problème a été posé par Henri Poincaré dans les méthodes nouvelles de la mécanique céleste. Le système dynamique en question est un système hamitonien, avec un terme perturbatif dont la période est un petit paramètre singulier et dont la taille est mesurée par un paramètre auxiliaire non singulier. (l'étude complète n'est menee à bien qu'au prix d'une simplification de ce terme). Comme Poincaré, nous décrivons les variétés stables et instables à l'aide de deux solutions de l'équation de HamiltonJacobi, trouvées en effectuant des développements convergents en puissances du paramètre non singulier. Ces solutions admettent le même développement asymptotique divergent par rapport au paramètre singulier, la divergence étant de type résurgent. Ceci permet de mesurer leur écart par la dérivation étrangère dont l'indice est le point singulier le plus proche de l'origine : on trouve un équivalent asymptotique exponentiellement petit par rapport au paramètre de perturbation singulière
Asymptotics in Dynamics, Geometry and PDEs ; Generalized Borel Summation vol. I by
Ovidiu Costin(
Book
)
1 edition published in 2011 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 5 WorldCat member libraries worldwide
Hyperbolicity of renormalization of critical circle maps by
Michael Yampolsky(
Book
)
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
Hyperbolicity of renormalization of critical circle maps. Nonamenable finitely presented torsionbycyclic groups / by Alexander
Yu. Ol'shanskii and Mark V. Sapir. by
Michael Yampolsky(
Book
)
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
Borel summation and splitting of separatrices for the Henon map by
Vasilij Gelʹfrejč(
Book
)
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Marmi, S. (Stefano) 1963 Other Author Editor
 Fauvet, F. (Frédéric) Other Editor
 Mitschi, C. (Claude) Other Author
 Marco, J.P
 Lochak, P. (Pierre) Author
 Manchon, Dominique Other Editor
 Costin, Ovidiu Author Editor
 Menous, Frédéric Editor
 Menous, F.
 LodayRichaud, Michèle Other
Associated Subjects
Asymptotic expansions Borel sets Continued fractions Diffeomorphisms Difference equations Differentiable dynamical systems Differential equations Differential equations, Parabolic Differential equations, Partial Divergent series Domains of holomorphy Dynamics Ergodic theory Functional equations Functions, Special Functions of complex variables Geometry, Differential Global analysis (Mathematics) Group theory Hamiltonian systems Integrals Invariant manifolds Lie groups Mappings (Mathematics) Mathematical physics Mathematics Monodromy groups Monogenic functions Painlevé equations Quantum theoryMathematics Quasianalytic functions Sequences (Mathematics) Small divisors Summability theory Symplectic geometry Symplectic groups Topological groups Transformations (Mathematics)