On the linearization of the generalized Ermakov 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.

References in corpus (2)

• On the Hamiltonian structure of Ermakov systems
• On the Lie symmetries of a class of generalized Ermakov systems

Cited by in corpus (11)

• Dynamical symmetries and the Ermakov invariant
• Anisotropic Bose-Einstein condensates and completely integrable dynamical systems
• Superposition rules for higher-order systems and their applications
• Generalized Hamiltonian structures for Ermakov systems
• Non-oscillating solutions to uncoupled Ermakov systems and the semiclassical limit
• Noetherian symmetries of noncentral forces with drag term
• Lie Point Symmetries for Reduced Ermakov Systems
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals
• On the Ermakov systems and nonlocal symmetries
• Three classes of Ermakov systems and nonlocal symmetries
• On the Lie symmetries of Kepler-Ermakov systems