Second edition. Great condition. Light shelf-wear along cover edges. Fore edge of text block is lightly smudged, but pages themselves are clean and unmarked.

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Bibliographic Details

Title

Geometrical Methods in the Theory of Ordinary Differential Equations

Publisher

Springer-Verlag

Publication Date

1988

Language

English

ISBN 10

3540780386

ISBN 13

9783540780380

Binding

Soft cover

Condition

Very good

Dust Jacket Condition

No jacket

Seller catalogs

Mathematics

About this title

Synopsis

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."

Language Notes

Text: English, Russian (translation)

"About this title" may belong to another edition of this title.

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