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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/319

Title: Renormalization Group for nonlinear oscillators in the absence of linear restoring force
Authors: Sarkar, A
Bhattacharjee, J K
Issue Date: 2010
Publisher: Europhys Lett
Citation: A. Sarkar and JKB, Renormalization group for nonlinear oscillators in the absence of linear restoring force, Europhys Lett, 2010, 91, 60004
Abstract: Perturbative Renormalization Group (RG) has been very useful in probing periodic orbits in two-dimensional dynamical systems (Sarkar A., Bhattacharjee J. K., Chakraborty S. and Banerjee D., arXiv:1005.2858v1 (2010)). The method relies on finding a linear center, around which perturbation analysis is done. However it is not obvious as to how systems devoid of any linear terms may be approached using this method. We propose here how RG can be done even in the absence of linear terms. We successfully apply the method to extract correct results for a variant of the second-order Riccati equation. In this variant the periodic orbit disappears as a parameter is varied. Our RG captures this disappearance correctly. We have also applied the technique successfully on the force-free Van der Pol-Duffing oscillator.
URI: http://hdl.handle.net/123456789/319
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