Download or read book The 21st Hilbert Problem for Linear Fuchsian Systems written by A. A. Bolibrukh and published by American Mathematical Soc.. This book was released on 1995 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bolibrukh presents the negative solution of Hilbert's twenty-first problem for linear Fuchsian systems of differential equations. Methods developed by Bolibrukh in solving this problem are then applied to the study of scalar Fuchsian equations and systems with regular singular points on the Riemmann sphere.
Download or read book The 21st Hilbert Problem for Linear Fuchsian Systems written by and published by . This book was released on 1998 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Riemann Hilbert Problem written by D. V. Anosov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.
Download or read book The Riemann Hilbert Problem written by D. V. Anosov and published by Vieweg+Teubner Verlag. This book was released on 1994-01-01 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.
Download or read book Divergent Series Summability and Resurgence I written by Claude Mitschi and published by Springer. This book was released on 2016-08-27 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability 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 “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear 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.
Download or read book The Stokes Phenomenon And Hilbert s 16th Problem written by B L J Braaksma and published by World Scientific. This book was released on 1996-05-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 16th Problem of Hilbert is one of the most famous remaining unsolved problems of mathematics. It concerns whether a polynomial vector field on the plane has a finite number of limit cycles. There is a strong connection with divergent solutions of differential equations, where a central role is played by the Stokes Phenomenon, the change in asymptotic behaviour of the solutions in different sectors of the complex plane.The contributions to these proceedings survey both of these themes, including historical and modern theoretical points of view. Topics covered include the Riemann-Hilbert problem, Painleve equations, nonlinear Stokes phenomena, and the inverse Galois problem.
Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Download or read book From Combinatorics to Dynamical Systems written by Frederic Fauvet and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine refereed research papers in various areas from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered include irregular connections, rank reduction and summability of solutions 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 interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.
Download or read book Linear Differential Equations in the Complex Domain written by Yoshishige Haraoka and published by Springer Nature. This book was released on 2020-11-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.
Download or read book Isomonodromic Deformations and Frobenius Manifolds written by Claude Sabbah and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
Download or read book Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics Proceedings Of The 5th International Workshop On Complex Structures And Vector Fields written by Stancho Dimiev and published by World Scientific. This book was released on 2001-08-02 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.
Download or read book Perspectives of Complex Analysis Differential Geometry and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2001 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Deligne-Simpson problem for zero index of rigidity / V.P. Rostov -- Theorems for extension on manifolds with almost complex structures / L.N. Apostolova, M.S. Marinov and K.P. Petrov -- The theorem on analytic representation on hypersurface with singularities / A.M. Kytmanov and S.G. Myslivets -- Pseudogroup structures on Spencer manifolds / S. Dimiev -- Type-changing transformations of Hurwitz pairs, quasiregular functions, and hyper Kahlerian holomorphic chains I / J. Lawrynowicz and L.M. Tovar -- Embedding of the moduli space of Riemann surfaces with Igeta structures into the Sato Grassmann manifold / Y. Hashimoto and K. Ohba -- On the quotient spaces of S2 x S2 under the natural action of subgroups of D4 / K. Kikuchi -- Existence of spin structures on cyclic branched covering spaces over four-manifolds / S. Nagami -- Length spectrum of geodesic spheres in rank one symmetric spaces / T. Adachi -- Grassmann geometry of 6-dimensional sphere, II / H. Hashimoto and K. Mashimo -- Hypersurfaces in Euclidean space which are one-parameter families of spheres / G. Ganchev and V. Mihova -- Hypersurfaces of conullity two in Euclidean space which are one-parameter systems of torses / G. Ganchev and V. Milousheva -- Real hypersurfaces of a Kaehler manifold (the sixteen classes) / G. Ganchev and M. Hristov -- Almost contact B-metric hypersurfaces of Kaehlerian manifolds with B-metric / M. Manev -- Projective formalism and some methods from algebraic geometry in the theory of gravitation / B.G. Dimitrov -- Geometry of manifolds and dark matter / I.B. Pestov -- Lagrangian fluid mechanics / S. Manoff -- Transformation of connectednesses / G. Zlatanov
Download or read book Hilbert G ttingen and the Development of Modern Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2019-02-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
Download or read book The Ball and Some Hilbert Problems written by Rolf-Peter Holzapfel and published by Birkhäuser. This book was released on 2012-12-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 prob lems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S pro gram. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21.
Download or read book Control Theory and Optimization I written by M.I. Zelikin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
Download or read book Special Functions written by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov and published by Oxford University Press, USA. This book was released on 2000 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a useful text and reference work.
Download or read book Trends in Complex Analysis Differential Geometry and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth International Workshop on Complex Structures and Vector Fields was a continuation of the previous five workshops (1992, 1994, 1996, 1998, 2000) on similar research projects. This series of workshops aims at higher achievements in studies of new research subjects. The present volume will meet with the satisfaction of many readers.
