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Global bifurcation theory and Hilbert's sixteenth problem /

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Bibliographic Details
Main Author:	Gaiko, Valery A.
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Boston : Kluwer Academic Publishers, [2003]
Series:	Mathematics and its applications (Kluwer Academic Publishers) ; v. 559.
Subjects:	Bifurcation theory. Vector fields. Polynomials. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Geometric Methods
On global bifurcation theory
Local bifurcations of limit cycles
On methods of the study of limit cycles
Geometric methods of bifurcations theory
Erugin's two-isocline method
On the method of isoclines
Isocline portraits
Classification of singular points
Other applications of the two-isocline method
The problem of center and focus
On the distinguishing problem
Lyapunov's focus quantities
Classification of symmetric cases
Geometric interpretation of quadratic centers
Poincare's topographical systems
Basic definitions
Construction of topographical systems
Topographical systems and limit cycles
On the control of semi-stable limit cycles
Canonical systems with limit cycles
Systems with field-rotation parameters
Reduction of quadratic systems
Andronov-Hopf Bifurcation
On the Andronov-Hopf bifurcation
On the history of the bifurcation
Bautin's result
The example by Shi Sonling
The example by E.A. Andronova
Construction of systems
Canonical systems with two singular points
Properties of the canonical systems
Bifurcations of limit cycles
Bifurcations of algebraic limit cycles
The case of a saddle and an antisaddle
A quadratic system with four limit cycles
Asymptotic behavior of limit cycles
Numerical results
Classification of Separatrix Cycles
On separatrix cycles
Dulac's theorem
Existential problem
On application of canonical systems
One saddle and three antisaddles (the first case).