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Author : Solomon Lefschetz
Publisher : Unknown
Page : 406 pages
File Size : 42,9 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015055721008
Geared toward upper-level undergraduates and graduate students, this text investigates nonlinear differential equations of the second order and includes an extensive overview of the classical literature. 1957 edition.
Author : S. Lefschetz
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:476309402
Author : V.I. Arnold
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210375
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.
Author : Jean Pierre Bourguignon,Paolo de Bartolomeis,Mariano Giaquinta
Publisher : Cambridge University Press
Page : 198 pages
File Size : 40,8 Mb
Release : 1998-05-28
Category : Mathematics
ISBN : 0521632463
This book gathers together papers from a workshop held in Cortona, Italy. The contributions come from a group of outstanding mathematicians and together they cover the most recent advances in the geometric theory of singular phenomena of partial differential equations occurring in real and complex differential geometry. This volume will be of great interest to all those whose research interests lie in real and complex differential geometry, partial differential equations, and gauge theory.
Author : Daniel Henry
Publisher : Springer
Page : 353 pages
File Size : 50,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385288
Author : Georges Valiron
Publisher : Math Science Press
Page : 834 pages
File Size : 54,7 Mb
Release : 1984
Category : Algebraic functions
ISBN : 0915692384
Author : Solomon Lefschetz
Publisher : Unknown
Page : 0 pages
File Size : 53,8 Mb
Release : 2005
Category : Differential equations
ISBN : 0486446492
Written by a celebrated mathematician and teacher, this text investigates nonlinear differential equations of the second order. Geared toward upper-level undergraduates and graduate students, it addresses problems that also concern professional mathematicians, physicists, and engineers. The first four chapters on preliminary questions, existence theorems, linear systems, and stability provide an extensive overview of the classical literature. The next three chapters deal with point stability, placing considerable emphasis on the fundamental work of Liapunov. Chapter 8 discusses periodic solutions, and subsequent chapters cover two-dimensional systems. Chapters 9 and 10 are devoted to the results of Poincar� and Bendixson: critical points, the index, behavior at infinity, and special systems. They also examine the important notion of structural stability and the contributions of Andronov-Pontrjagin and DeBaggis. The last two chapters concern equations of the second order--notably, the work of Cartwright-Littlewood, Levinson-Smith, and Levinson--and the application of the perturbation method. Two appendices--one on vectors and matrices, and the other on topology--conclude the text, along with a supplemental list of problems.
Author : Agostino Prastaro
Publisher : World Scientific
Page : 764 pages
File Size : 43,7 Mb
Release : 1996
Category : Science
ISBN : 9810225202
This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.
Author : Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Publisher : Springer
Page : 216 pages
File Size : 43,7 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319740423
This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Author : Jane Cronin
Publisher : CRC Press
Page : 408 pages
File Size : 44,9 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9781420014938
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
Author : Christian Pötzsche
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 40,5 Mb
Release : 2010-09-17
Category : Mathematics
ISBN : 9783642142574
The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Author : P.H. Kersten,I.S. Krasil'shchik
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400901797
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
Author : Peter J. Vassiliou,Ian G. Lisle
Publisher : Cambridge University Press
Page : 242 pages
File Size : 48,5 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521775981
A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.
Author : Valentin Lychagin,Joseph Krasilshchik
Publisher : MDPI
Page : 204 pages
File Size : 47,5 Mb
Release : 2021-09-03
Category : Mathematics
ISBN : 9783036510460
This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Author : Jeremy Gray
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 40,7 Mb
Release : 2010-01-07
Category : Mathematics
ISBN : 9780817647735
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.