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An Algebraic Approach to the Classification of Centers in Polynomial Liénard Systems

✍ Scribed by Colin Christopher

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
87 KB
Volume
229
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider the second-order Liénard system

where f x and g x are polynomials, which we rewrite in the equivalent twodimensional form,

We show that the local question of whether a critical point of this system is a center can be expressed in terms of global conditions on f and g. Using these results, we give a simple classification of all such centers. We also address the problem of the coexistence of centers, foci, and limit cycles for these systems. Systems with degenerate centers are also considered.

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