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Uniformly isochronous centers of polynomial systems in \(\mathbb{R}^ 2\). (English) Zbl 0795.34021

Elworthy, K.D. (ed.) et al., Differential equations, dynamical systems, and control science. A Festschrift in Honor of Lawrence Markus. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 152, 21-31 (1994).
A centre is said to be isochronous if the period of each closed path surrounding the (isolated) centre is constant. The centre is said to be uniformly isochronous if the angular velocity of the ray from the centre to a point on a cycle is the same for every cycle. The author discusses the existence of such centres for the system \(\dot x= X(x,y)\), \(\dot y= Y(x,y)\) where \(X(x,y)\) and \(Y(x,y)\) are polynomials in \(x\) and \(y\).
For the entire collection see [Zbl 0780.00045].
Reviewer: P.Smith (Keele)

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
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