Renormalization group and isochronous oscillations
Amartya Sarkar, J. K. Bhattacharjee
TL;DR
This paper explores the application of renormalization group techniques to analyze isochronicity in two-dimensional dynamical systems, deriving necessary conditions for specific classes like Cherkas and cubic systems, aligning with recent studies.
Contribution
It introduces a novel RG-based framework for studying isochronicity and provides necessary conditions for certain classes of systems, advancing theoretical understanding.
Findings
Necessary conditions for isochronicity in Cherkas systems
Necessary conditions for isochronicity in cubic systems
Conditions satisfied by recent studied cases
Abstract
We show how the condition of isochronicity can be studied for two dimensional systems in the renormalization group (RG) context. We find a necessary condition for the isochronicity of the Cherkas and another class of cubic systems. Our conditions are satisfied by all the cases studied recently by Bardet et al \cite{bard} and Ghose Choudhury and Guha
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