Recursive Generation of Isochronous Hamiltonian Systems

TL;DR

This paper introduces a recursive method to generate a sequence of isochronous Hamiltonian systems by identifying a collective coordinate, enabling the creation of multiple oscillators with identical periods.

Contribution

The paper presents a novel recursive procedure for constructing isochronous Hamiltonians, expanding the class of such systems through a systematic identification of collective coordinates.

Findings

Successfully generates an infinite sequence of isochronous oscillators.

Provides a simple, recursive method for constructing isochronous Hamiltonians.

Enhances understanding of collective coordinates in Hamiltonian dynamics.

Abstract

We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively.