Geometrical Methods In The Theory Of Ordinary Differential Equations
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Geometrical Methods In The Theory Of Ordinary Differential Equations
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometrical Methods In The Theory Of Ordinary Differential Equations written by V.I. Arnold 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 2012-12-06 with Mathematics categories.
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.
Geometrical Methods In The Theory Of Ordinary Differential Equations
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: Springer
Release Date : 1988
Geometrical Methods In The Theory Of Ordinary Differential Equations written by Vladimir Igorevich Arnolʹd and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Geometrical Methods In The Theory Of Ordinary Differential Equations
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Author : V.I. Arnold
language : en
Publisher: Springer
Release Date : 1988
Geometrical Methods In The Theory Of Ordinary Differential Equations written by V.I. Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Since 1978, when the first Russian edition of this book appeared, geometrical methods in the theory of ordinary differential equations have become very popular. A lot of computer experiments have been performed and some theorems have been proved. In this edition, this progress is (partially) repre sented by some additions to the first English text. I mention here some of these recent discoveries. I. The Feigenbaum universality of period doubling cascades and its extensions- the renormalization group analysis of bifurcations (Percival, Landford, Sinai, ... ). 2. The Zol~dek solution of the two-parameter bifurcation problem (cases of two imaginary pairs of eigenvalues and of a zero eigenvalue and a pair). 3. The Iljashenko proof of the "Dulac theorem" on the finiteness of the number of limit cycles of polynomial planar vector fields. 4. The Ecalle and Voronin theory of hoi om orphic invariants for formally equivalent dynamical systems at resonances. 5. The Varchenko and Hovanski theorems on the finiteness of the number of limit cycles generated by a polynomial perturbation of a poly nomial Hamiltonian system (the Dulac form of the weakened version of Hilbert's sixteenth problem). 6. The Petrov estimates of the number of zeros of the elliptic integrals responsible for the birth of limit cycles for polynomial perturbations 2 of the Hamiltonian system x = x - I (solution of the weakened sixteenth Hilbert problem for cubic Hamiltonians). 7. The Bachtin theorems on averaging in systems with several frequencies.
Ordinary Differential Equations
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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-05-08
Ordinary Differential Equations written by Vladimir I. Arnold 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 1992-05-08 with Mathematics categories.
Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW
Ordinary Differential Equations
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Author : Vladimir Igorevich Arnolʹd
language : en
Publisher: Mit Press
Release Date : 1978
Ordinary Differential Equations written by Vladimir Igorevich Arnolʹd and has been published by Mit Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises. In the terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of one-parameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental concepts--like phase space and phase flows, smooth manifolds and tangent bundles, vector fields and one-parameter groups of diffeomorphisms--that remain in the shadows in the traditional coordinate-based approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra.
Nonlinear Ordinary Differential Equations
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Author : Dominic William Jordan
language : en
Publisher: Oxford University Press, USA
Release Date : 1999
Nonlinear Ordinary Differential Equations written by Dominic William Jordan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos.
Geometric Numerical Integration
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Geometric Numerical Integration written by Ernst Hairer 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 2013-03-09 with Mathematics categories.
This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Ordinary Differential Equations
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Author : Vladimir Igorevich Arnol'd
language : en
Publisher:
Release Date : 1973
Ordinary Differential Equations written by Vladimir Igorevich Arnol'd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Differential equations categories.
Ordinary Differential Equations With Applications
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Author : Sze-Bi Hsu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-06-07
Ordinary Differential Equations With Applications written by Sze-Bi Hsu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Mathematics categories.
During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE). This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques. Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers. This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
Geometric Methods In System Theory
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Author : D.Q. Mayne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Methods In System Theory written by D.Q. Mayne 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 2012-12-06 with Science categories.
Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints. Examples are numerous; in a switched, lossless electrical network energy is conserved and the state evolves on an ellipsoid surface defined by x'Qx equals a constant; in the control of finite state, continuous time, Markov processes the state evolves on the set x'x = 1, xi ~ O. The control of rigid body motions and trajectory control leads to problems of this type. There has been under way now for some time an effort to build up enough control theory to enable one to treat these problems in a more or less routine way. It is important to emphasise that the ordinary vector space-linear theory often gives the wrong insight and thus should not be relied upon.