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.
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This review is from: Geometrical Methods in the Theory of Ordinary Differential Equations (Grundlehren der mathematischen Wissenschaften) (v. 250) (Hardcover)
The only way to understand the basic idea of V.I. Arnol'd in this splendid - yet very difficult book - is to read carefully the following text: [...]
We are inside a deep educational crisis forbidding to the students to establish close intellectual contact with their scientific ancestors.
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In the study of differential equations, methods from all fields of mathematics are used. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
decrement diagram, expanding foliations, closed phase curve, zeroth section, weak transversality theorem, homological equation, characteristic direction field, contracting foliation, algebraic unsolvability, discriminant curve, maximal real part, formal normal form, monodromy operator, nondegenerate pair, degenerate singular point, convergent fraction, soft loss, vanishing roots, miniversal deformations, averaged system, initial manifold, everywhere dense set, equivariant vector fields, rational rotation number, structurally stable systems Key Phrases - Capitalized Phrases (CAPs): (learn more)
Local Bifurcation Theory, New York, Implicit Differential Equation, Uspekhi Mat, Additional Problems, Pure Appl, The Case of Symmetry of Order, Trudy Sem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In the study of differential equations, methods from all fields of mathematics are used. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
decrement diagram, expanding foliations, closed phase curve, zeroth section, weak transversality theorem, homological equation, characteristic direction field, contracting foliation, algebraic unsolvability, discriminant curve, maximal real part, formal normal form, monodromy operator, nondegenerate pair, degenerate singular point, convergent fraction, soft loss, vanishing roots, miniversal deformations, averaged system, initial manifold, everywhere dense set, equivariant vector fields, rational rotation number, structurally stable systems Key Phrases - Capitalized Phrases (CAPs): (learn more)
Local Bifurcation Theory, New York, Implicit Differential Equation, Uspekhi Mat, Additional Problems, Pure Appl, The Case of Symmetry of Order, Trudy Sem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 72
books:
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100
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- Differential Equations (2nd Edition) by John Polking in Front Matter (1), Front Matter (2), and page 74
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Front Matter (1), and Front Matter (2)
- Ordinary Differential Equations by V.I. Arnold in Front Matter (1), and Front Matter (2)
- Entropy, Large Deviations, and Statistical Mechanics (Classics in Mathematics) by Richard Ellis in Back Matter
- Sheaves on Manifolds: With a Short History "Les debuts de la theorie des faisceaux" by Christian Houzel (Grundlehren der mathematischen Wissenschaften) by Masaki Kashiwara in Back Matter
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- Vorlesungen über partielle Differentialgleichungen (Springer-Lehrbuch) (German Edition) by Vladimir I. Arnold on page 11, and page 23
- Normal Forms, Bifurcations and Finiteness Problems in Differential Equations (NATO Science Series II: Mathematics, Physics and Chemistry) by Gert Sabidussi on page 314, and page 350
- Nonlinear Dynamics: A Two-Way Trip from Physics to Math by H.G Solari on page 82, and Back Matter
- Lectures on Partial Differential Equations (Universitext) by Vladimir I. Arnold on page 10, and page 20
- Dynamical Systems Approach to Turbulence (Cambridge Nonlinear Science Series) by Tomas Bohr in Back Matter
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