Geometrical Methods in the Theory of Ordinary Differential Equations

Arnold, V.I.:

ISBN 10: 3540780386 / ISBN 13: 9783540780380

Editore: Springer, 1988

Riguardo questo articolo

351 Seiten; Das Buch befindet sich in einem gut erhaltenen Zustand. In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 645. Codice articolo 2143183

Dati bibliografici

Titolo: Geometrical Methods in the Theory of ...

Casa editrice: Springer

Data di pubblicazione: 1988

Legatura: Broschiert

Condizione: Gut

Edizione: 2. Auflage;.

Descrizione articolo

Riassunto:

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.

Contenuti:

1 Special Equations.- 2 First-Order Partial Differential Equations.- 3 Structural Stability.- 4 Perturbation Theory.- 5 Normal Forms.- 6 Local Bifurcation Theory.- Samples of Examination Problems.