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The Stokes Phenomenon And Hilbert S 16th Problem

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The Stokes Phenomenon And Hilbert S 16th Problem

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Author : B L J Braaksma
language : en
Publisher: World Scientific
Release Date : 1996-05-06

The Stokes Phenomenon And Hilbert S 16th Problem written by B L J Braaksma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-06 with categories.

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.

The Stokes Phenomenon And Hilbert S 16th Problem

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Author : Boele Lieuwe Jan Braaksma
language : en
Publisher:
Release Date : 1996

The Stokes Phenomenon And Hilbert S 16th Problem written by Boele Lieuwe Jan Braaksma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Airy functions categories.

Planar Dynamical Systems

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Author : Yirong Liu
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-29

Planar Dynamical Systems written by Yirong Liu and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.

In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

Differential Equations And The Stokes Phenomenon

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Author : B L J Braaksma
language : en
Publisher: World Scientific
Release Date : 2002-12-10

Differential Equations And The Stokes Phenomenon written by B L J Braaksma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-10 with Mathematics categories.

This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.

Concerning The Hilbert 16th Problem

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Author : S. Yakovenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Concerning The Hilbert 16th Problem written by S. Yakovenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Differential equations categories.

Proceedings Of The Conference On Differential Equations And The Stokes Phenomenon

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Author : Boele Lieuwe Jan Braaksma
language : en
Publisher: World Scientific
Release Date : 2002

Proceedings Of The Conference On Differential Equations And The Stokes Phenomenon written by Boele Lieuwe Jan Braaksma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.

Differential Geometry And Physics

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Author : Mo-Lin Ge
language : en
Publisher: World Scientific
Release Date : 2006

Differential Geometry And Physics written by Mo-Lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory. Sample Chapter(s). Chapter 1: Yangian and Applications (787 KB). Contents: Yangian and Applications (C-M Bai et al.); The Hypoelliptic Laplacian and the ChernOCoGaussOCoBonnet (J-M Bismut); S S Chern and ChernOCoSimos Terms (R Jackiw); Localization and Conjectures from String Duality (K F Liu); Topologization of Electron Liquids with ChernOCoSimons Theory and Quantum Computation (Z H Wang); Topology and Quantum Information (L H Kauffman); Toeplitz Quantization and Symplectic Reduction (X N Ma & W P Zhang); Murphy Operators in Knot Theory (H R Morton); Separation Between Spin and Charge in SU(2) YangOCoMills Theory (A J Niemi); LAwner Equations and Dispersionless Hierarchies (K Takasaki & T Takebe); and other papers. Readership: Graduate students and professional researchers in geometry and physics."

Differential Geometry And Physics Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics

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Author : Weiping Zhang
language : en
Publisher: World Scientific
Release Date : 2006-12-11

Differential Geometry And Physics Proceedings Of The 23th International Conference Of Differential Geometric Methods In Theoretical Physics written by Weiping Zhang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-11 with Mathematics categories.

Normal Forms Bifurcations And Finiteness Problems In Differential Equations

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Author : Christiane Rousseau
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29

Normal Forms Bifurcations And Finiteness Problems In Differential Equations written by Christiane Rousseau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-29 with Mathematics categories.

Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002

Painlev Transcendents

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Author : Athanassios S. Fokas
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-20

Painlev Transcendents written by Athanassios S. Fokas and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-20 with Mathematics categories.

At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I–VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these “nonlinear special functions”. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas.

The Stokes Phenomenon And Hilbert S 16th Problem

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