On the linearization of the generalized Ermakov systems

TL;DR

This paper introduces a linearization method for generalized Ermakov systems with variable-dependent frequencies, broadening the class of systems that can be linearized similarly to traditional Ermakov systems, including Kepler--Ermakov systems.

Contribution

A new linearization procedure applicable to a wide class of generalized Ermakov systems with variable-dependent frequencies is proposed, extending the linearization approach beyond traditional systems.

Findings

The procedure applies to Kepler--Ermakov systems.

It includes more generic systems beyond classical Ermakov systems.

The method simplifies analysis of complex dynamical systems.

Abstract

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included.