Mitschi, C. (Claude)
Overview
Works:  14 works in 52 publications in 3 languages and 1,658 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Thesis advisor 
Publication Timeline
.
Most widely held works by
C Mitschi
From combinatorics to dynamical systems : journées de calcul formel, Strasbourg, March 2223, 2002 by
F Fauvet(
)
14 editions published between 2003 and 2008 in English and held by 1,270 WorldCat member libraries worldwide
This book contains nine refereed research papers in various areas, from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered are irregular connections, summability of solutions and rank reduction of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi polynomial formalism, Padé approximants related to analytic integrability, hybrid systems. The volume as a whole gives a presentation of productive interactions between ideas stemming from computer algebra and questions arising in dynamical systems or combinatorics. As such, it should be useful for both mathematicians and theoretical physicists who are interested in effective computation
14 editions published between 2003 and 2008 in English and held by 1,270 WorldCat member libraries worldwide
This book contains nine refereed research papers in various areas, from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered are irregular connections, summability of solutions and rank reduction of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi polynomial formalism, Padé approximants related to analytic integrability, hybrid systems. The volume as a whole gives a presentation of productive interactions between ideas stemming from computer algebra and questions arising in dynamical systems or combinatorics. As such, it should be useful for both mathematicians and theoretical physicists who are interested in effective computation
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
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
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
Differential equations and quantum groups : Andrey A. Bolibrukh memorial volume by
DANIEL BERTRAND; BENJAMIN ENRIQUEZ; CLAUDE MITSCHI(
)
2 editions published between 2006 and 2007 in English and held by 19 WorldCat member libraries worldwide
This special volume is dedicated to the memory of Andrey A. Bolibrukh. It contains two expository articles devoted to some aspects of Bolibrukh's work, followed by ten refereed research articles. Topics cover complex linear and nonlinear differential equations as well as quantum groups: monodromy, Fuchsian linear systems, RiemannHilbert problem, differential Galois theory, differential algebraic groups, multisummability, isomonodromy, Painlevé equations, Schlesinger equations, integrable systems, KZ equations, complex reflection groups, root systems
2 editions published between 2006 and 2007 in English and held by 19 WorldCat member libraries worldwide
This special volume is dedicated to the memory of Andrey A. Bolibrukh. It contains two expository articles devoted to some aspects of Bolibrukh's work, followed by ten refereed research articles. Topics cover complex linear and nonlinear differential equations as well as quantum groups: monodromy, Fuchsian linear systems, RiemannHilbert problem, differential Galois theory, differential algebraic groups, multisummability, isomonodromy, Painlevé equations, Schlesinger equations, integrable systems, KZ equations, complex reflection groups, root systems
Groupes de galois differentiels et Gfonctions by
C Mitschi(
Book
)
4 editions published in 1989 in French and held by 15 WorldCat member libraries worldwide
DANS CETTE THESE NOUS DETERMINONS LE GROUPE DE GALOIS DIFFERENTIEL DE CERTAINES EQUATIONS HYPERGEOMETRIQUES CONFLUENTES GENERALISEES. CES EQUATIONS, QUI ADMETTENT COMME SOLUTIONS LES GFONCTIONS DE MEIJER, ONT LA PARTICULARITE DE PRESENTER DEUX SINGULARITES, L'UNE REGULIERE, L'AUTRE IRREGULIERE. NOUS DONNONS, OUTRE DES CONDITIONS D'IRREDUCTIBILITE PORTANT SUR LES PARAMETRES DES EQUATIONS, DES CONDITIONS PERMETTANT D'OBTENIR DES GROUPES CLASSIQUES
4 editions published in 1989 in French and held by 15 WorldCat member libraries worldwide
DANS CETTE THESE NOUS DETERMINONS LE GROUPE DE GALOIS DIFFERENTIEL DE CERTAINES EQUATIONS HYPERGEOMETRIQUES CONFLUENTES GENERALISEES. CES EQUATIONS, QUI ADMETTENT COMME SOLUTIONS LES GFONCTIONS DE MEIJER, ONT LA PARTICULARITE DE PRESENTER DEUX SINGULARITES, L'UNE REGULIERE, L'AUTRE IRREGULIERE. NOUS DONNONS, OUTRE DES CONDITIONS D'IRREDUCTIBILITE PORTANT SUR LES PARAMETRES DES EQUATIONS, DES CONDITIONS PERMETTANT D'OBTENIR DES GROUPES CLASSIQUES
Matrices de stokes et groupe de Galois des équations hypergéométriques confluentes généralisées by
Anne Duval(
Book
)
2 editions published in 1988 in Undetermined and French and held by 9 WorldCat member libraries worldwide
2 editions published in 1988 in Undetermined and French and held by 9 WorldCat member libraries worldwide
Exposants, réseaux de levelt et relations de Fuchs pour les systèmes différentiels réguliers by
EDUARDO COREL(
Book
)
2 editions published in 1999 in French and held by 5 WorldCat member libraries worldwide
Dans cette these nous generalisons la relation de Fuchs, verifiee par les exposants d'une equation differentielle Fuchsienne, au cas des systemes differentiels lineaires a points singuliers reguliers sur P 1. Cette generalisation, qui prend la forme d'un encadrement de la somme des exposants, resulte d'une etude locale de la connexion reguliere que l'on peut associer au systeme. Nous montrons que la notion analytique d'exposants d'un systeme differentiel developpee par Levelt est un invariant algebrique du reseau attache au systeme. Plus precisement, les exposants representent les valeurs propres du residu de la connexion par rapport a un certain reseau stable maximal que nous definissons, et que nous appelons reseau de Levelt du reseau precedent. Les problemes relatifs aux exposants se traduisent en termes de diviseurs elementaires de modules sur un anneau principal. Nous determinons ainsi les bornes de l'inegalite de Fuchs pour les systemes. Cette interpretation algebrique nous permet egalement de preciser les principaux resultats connus sur les exposants (Gantmacher, Levelt, Bolibrukh). Nous appliquons ensuite ces methodes a l'etude des constructions tensorielles d'un systeme donne. Nous illustrons enfin les resultats precedents par des exemples numeriques que nous traitons a l'aide du logiciel Maple en appliquant une idee de Gerard et Levelt. Nous obtenons des approximations de la valeur des exposants, et, dans certains cas, leur valeur exacte
2 editions published in 1999 in French and held by 5 WorldCat member libraries worldwide
Dans cette these nous generalisons la relation de Fuchs, verifiee par les exposants d'une equation differentielle Fuchsienne, au cas des systemes differentiels lineaires a points singuliers reguliers sur P 1. Cette generalisation, qui prend la forme d'un encadrement de la somme des exposants, resulte d'une etude locale de la connexion reguliere que l'on peut associer au systeme. Nous montrons que la notion analytique d'exposants d'un systeme differentiel developpee par Levelt est un invariant algebrique du reseau attache au systeme. Plus precisement, les exposants representent les valeurs propres du residu de la connexion par rapport a un certain reseau stable maximal que nous definissons, et que nous appelons reseau de Levelt du reseau precedent. Les problemes relatifs aux exposants se traduisent en termes de diviseurs elementaires de modules sur un anneau principal. Nous determinons ainsi les bornes de l'inegalite de Fuchs pour les systemes. Cette interpretation algebrique nous permet egalement de preciser les principaux resultats connus sur les exposants (Gantmacher, Levelt, Bolibrukh). Nous appliquons ensuite ces methodes a l'etude des constructions tensorielles d'un systeme donne. Nous illustrons enfin les resultats precedents par des exemples numeriques que nous traitons a l'aide du logiciel Maple en appliquant une idee de Gerard et Levelt. Nous obtenons des approximations de la valeur des exposants, et, dans certains cas, leur valeur exacte
Groupes de Galois différentiels et Gfonctions by
Claude Mitschi(
Book
)
1 edition published in 1989 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 1989 in French and held by 4 WorldCat member libraries worldwide
Connected linear groups as differential Galois groups by
Claudine Mitschi(
Book
)
3 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
Groupes de galois differentiels et Gfonctions by
Claude Mitschi(
Book
)
1 edition published in 1989 in Undetermined and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in Undetermined and held by 2 WorldCat member libraries worldwide
Differential Equations and Quantum Groups(
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
Some applications of parameterized Picard–Vessiot theory(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: This is an expository article describing some applications of parameterized Picard–Vessiot theory. This Galois theory for parameterized linear differential equations was Cassidy and Singer's contribution to an earlier volume dedicated to the memory of Andrey Bolibrukh. The main results we present here were obtained for families of ordinary differential equations with parameterized regular singularities in joint work with Singer. They include parametric versions of Schlesinger's theorem and of the weak Riemann–Hilbert problem as well as an algebraic characterization of a special type of monodromy evolving deformations illustrated by the classical Darboux–Halphen equation. Some of these results have recently been applied by different authors to solve the inverse problem of parameterized Picard–Vessiot theory, and were also generalized to irregular singularities. We sketch some of these results by other authors. The paper includes a brief history of the Darboux–Halphen equation as well as an appendix on differentially closed fields
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Abstract: This is an expository article describing some applications of parameterized Picard–Vessiot theory. This Galois theory for parameterized linear differential equations was Cassidy and Singer's contribution to an earlier volume dedicated to the memory of Andrey Bolibrukh. The main results we present here were obtained for families of ordinary differential equations with parameterized regular singularities in joint work with Singer. They include parametric versions of Schlesinger's theorem and of the weak Riemann–Hilbert problem as well as an algebraic characterization of a special type of monodromy evolving deformations illustrated by the classical Darboux–Halphen equation. Some of these results have recently been applied by different authors to solve the inverse problem of parameterized Picard–Vessiot theory, and were also generalized to irregular singularities. We sketch some of these results by other authors. The paper includes a brief history of the Darboux–Halphen equation as well as an appendix on differentially closed fields
Sur la réductibilité des systèmes fuchsiens by
Stéphane Malek(
Book
)
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
DANS CETTE THESE NOUS ETABLISSONS DEUX RESULTATS CONCERNANT LA REDUCTIBILITE DES SYSTEMES DIFFERENTIELS LINEAIRES FUCHSIENS SUR LA SPHERE DE RIEMANN. NOUS MONTRONS QUE TOUT SYSTEME FUCHSIEN AYANT UNE REPRESENTATION DE MONODROMIE REDUCTIBLE EST EQUIVALENT A UN SYSTEME FUCHSIEN DONT LES MATRICES DE COEFFICIENTS RELATIVES AUX DIFFERENTS POLES SONT SIMULTANEMENT REDUCTIBLES. LORSQUE LA REPRESENTATION DE MONODROMIE D'UN SYSTEME FUCHSIEN EST UNE SOMME DIRECTE DE DEUX REPRESENTATIONS, NOUS MONTRONS QUE L'ON PEUT REALISER CHAQUE TERME DE CETTE SOMME COMME UNE REPRESENTATION DE MONODROMIE D'UN SYSTEME FUCHSIEN. NOUS APPLIQUONS ENSUITE CES RESULTATS A LA CONSTRUCTION DE NOUVEAUX CONTREEXEMPLES AU PROBLEME DE RIEMANNHILBERT
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
DANS CETTE THESE NOUS ETABLISSONS DEUX RESULTATS CONCERNANT LA REDUCTIBILITE DES SYSTEMES DIFFERENTIELS LINEAIRES FUCHSIENS SUR LA SPHERE DE RIEMANN. NOUS MONTRONS QUE TOUT SYSTEME FUCHSIEN AYANT UNE REPRESENTATION DE MONODROMIE REDUCTIBLE EST EQUIVALENT A UN SYSTEME FUCHSIEN DONT LES MATRICES DE COEFFICIENTS RELATIVES AUX DIFFERENTS POLES SONT SIMULTANEMENT REDUCTIBLES. LORSQUE LA REPRESENTATION DE MONODROMIE D'UN SYSTEME FUCHSIEN EST UNE SOMME DIRECTE DE DEUX REPRESENTATIONS, NOUS MONTRONS QUE L'ON PEUT REALISER CHAQUE TERME DE CETTE SOMME COMME UNE REPRESENTATION DE MONODROMIE D'UN SYSTEME FUCHSIEN. NOUS APPLIQUONS ENSUITE CES RESULTATS A LA CONSTRUCTION DE NOUVEAUX CONTREEXEMPLES AU PROBLEME DE RIEMANNHILBERT
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Fauvet, F. (Frédéric) Author Editor
 Sauzin, D. 1966 Other
 LodayRichaud, Michèle Other
 Delabaere, Éric
 Bertrand, D. (Daniel) Thesis advisor Editor
 Sabbah, Claude Editor
 Enriquez, Benjamin Editor
 Schäfke, Reinhard Editor
 Bolibrukh, A. A. Thesis advisor
 Duval, Anne Author
Associated Subjects
AlgebraData processing Bolibrukh, A. A Difference equations Differential equations Divergent series Dynamics Ergodic theory Functional equations Functions, Special Functions of complex variables Lie groups Mathematics Monodromy groups Painlevé equations Quantum groups RiemannHilbert problems Sequences (Mathematics) Summability theory Topological groups