ON THE ISOCHRONICITY OF PERIODIC SOLUTIONS AT A CENTRE MANIFOLD
Abstract
The problem of isochronicity is discussed from the historical and dynamical systems point of view. The model of Huygen’s cycloidal chops is mathematically explained. We consider two dynamical systems arising from a three-dimensional system with a centre manifold. Based on the period function approach we find necessary and sufficient criteria on the coefficients of the system to distinguish between the cases of isochronous and non-isochronous oscillations.
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References
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