Isochronous Centers of Lienard Type Equations and Applications
A. Raouf Chouikha
Abstract
In this work we study the equation (E) x + f(x) x2 + g(x) = 0 with a center at 0 and investigate conditions of its isochronicity. When f and g are analytic (not necessary odd) a necessary and sufficient condition for the isochronicity of 0 is given. This approach allows us to present an algorithm for obtained conditions for a point of (E) to be an isochronous center. In particular, we find again by another way the isochrones of the quadratic Loud systems (LD,F). Some classes of Kukles are also considered. Moreover, we classify a 5-parameters family of reversible cubic systems with isochronous centers. Key Words and phrases: period function, monotonicity, isochronicity, center, polynomial systems.
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