Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006 This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide with the entire set of all initial data), from which emerge solutions all of which are completely periodic (i.e ...
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From isochronous potentials to isochronous systems
Journal of Differential Equations, 2015 This paper studies Hamiltonian systems of the type \[ \left\{ \begin{align*}{ \dot{y}&= - V'(x) \cr \dot{x}&= T'(y) ,}\end{align*} \right. \] where \(T\) and \(V\) are \(C^2\)-functions, with associated Hamiltonian function \[ E(x,y) = T(y) + V(x). \] The system is assumed to have a center at a certain point \((x_0,y_0)\), and \(V(x_0) = T(y_0) = 0 ...
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