论文信息 - Isochronicity of analytic systems via Urabe's criterion

Isochronicity of analytic systems via Urabe's criterion

A method for studying isochronous oscillations in some systems of ODE reducible to the equation is described. It is applied to obtain the necessary and sufficient conditions for isochronicity of a cubic two-dimensional autonomous system depending on six parameters. For all isochronous systems in this family the Urabe function is explicitly constructed.

Valery G. Romanovski | Xingwu Chen | A. Raouf Chouikha

[1] Marco Sabatini,et al. ON THE PERIOD FUNCTION OF LIENARD SYSTEMS , 1999 .

[2] Valery G. Romanovski,et al. The centre and isochronicity problems for some cubic systems , 2001 .

[3] Colin Christopher,et al. On the classification of Liénard systems with amplitude-independent periods , 2004 .

[4] V. Romanovski,et al. On Urabe's criteria of isochronicity , 2000, nlin/0003065.

[5] J. Chavarriga,et al. Isochronous centers of cubic reversible systems , 1999 .

[6] Marco Sabatini,et al. A survey of isochronous centers , 1999 .

[7] M. Urabe. The potential force yielding a periodic motion whose period is an arbitrary continuous function of the amplitude of the velocity , 1962 .

[8] M. Sabatini. On the period function of x″+f(x)x′2+g(x)=0 , 2004 .

[9] On the quantum spectrum of isochronous potentials , 2005, quant-ph/0504074.

[10] P. Ponzo. Nonlinear Oscillations in a Second Order System , 1964 .