Nonlinear Phenomena in Complex Systems, 2003, Vol.6, No.1, pp.577-581

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2003, Vol.6, No.1, pp.577-581

Abelian Integrals and Limit Cycles in Polynomial Dynamical Systems
Valery A. Gaiko

Two-dimensional polynomial dynamical systems are considered. Earlier we suggested two different approaches to the second part of Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The first approach is bifurcational, and it is based on the ideas of the global qualitative investigation. The second one is algebraic, and it is based on the ideas solving a so-called "inverse problem'' of the dynamical systems. In this paper, we discuss the third approach which is based on the method of Abelian integrals.
Key words: Polynomial dynamical system, Abelian integral, Limit cycle

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