Geometrical Methods In The Theory Of Ordinary Differential Equations

Author : V.I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1461210372
Total Pages : 366 pages
Book Rating : 4.75/5 ( download)

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Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vladimir Igorevich Arnolʹd
Publisher : Springer
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.60/5 ( download)

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Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by Vladimir Igorevich Arnolʹd and published by Springer. This book was released on 1988 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : V.I. Arnold
Publisher : Springer
ISBN 13 : 9783662118320
Total Pages : 0 pages
Book Rating : 4.27/5 ( download)

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Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer. This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 9783540548133
Total Pages : 346 pages
Book Rating : 4.30/5 ( download)

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Download or read book Ordinary Differential Equations written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 1992-05-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : V.I. Arnold
Publisher : National Geographic Books
ISBN 13 : 0262510189
Total Pages : 0 pages
Book Rating : 4.89/5 ( download)

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Download or read book Ordinary Differential Equations written by V.I. Arnold and published by National Geographic Books. This book was released on 1978-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 : 3662050188
Total Pages : 526 pages
Book Rating : 4.87/5 ( download)

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Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Agostino Prastaro
Publisher : World Scientific
ISBN 13 : 9789810214074
Total Pages : 482 pages
Book Rating : 4.73/5 ( download)

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Download or read book Geometry in Partial Differential Equations written by Agostino Prastaro and published by World Scientific. This book was released on 1994 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Author : Vladimir Igorevich Arnold
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.80/5 ( download)

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Download or read book Ordinary Differential Equations written by Vladimir Igorevich Arnold and published by . This book was released on 1978 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alessio Figalli
Publisher : Springer
ISBN 13 : 3319740423
Total Pages : 216 pages
Book Rating : 4.23/5 ( download)

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Download or read book Partial Differential Equations and Geometric Measure Theory written by Alessio Figalli and published by Springer. This book was released on 2018-05-23 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
ISBN 13 : 9783037190500
Total Pages : 224 pages
Book Rating : 4.07/5 ( download)

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Download or read book Lectures on Differential Geometry written by Iskander Asanovich Taĭmanov and published by European Mathematical Society. This book was released on 2008 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.