Eur. Phys. J. D 61, 443-448 (2011)
https://doi.org/10.1140/epjd/e2010-00281-6

Counting limit cycles with the help of the renormalization group

¹ Department of Mathematics, South Point High School, Kolkata, India
² Department of Physics, Jadavpur University, 700032 Kolkata, India
³ S.N. Bose National Centre for Basic Sciences, Kolkata, India

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Received: 10 June 2010
Revised: 4 August 2010
Published online: 10 November 2010

Abstract

We use the renormalization group to set up an easy algorithm for finding the amplitude equation for an arbitrary two dimensional dynamical system of the Liénard type. This allows us to address the second part of Hilbert's sixteenth problem, at least in the weak damping limit.