Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces

Abstract

Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By means of the Poincaré-Pontryagin theory, the existence of limit cycles on the invariant Casimir surfaces for the perturbed system is investigated up to first order of perturbation, providing sharp bounds for their number. Examples are given.

References in corpus (3)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• Characterization and global analysis of a family of Poisson structures
• An integrable family of Poisson systems: Characterization and global analysis

Cited by in corpus (6)

• Inverse Jacobi multiplier as a link between conservative systems and Poisson structures
• Periodic orbits in analytically perturbed Poisson systems
• Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces
• Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems
• New global solutions of the Jacobi partial differential equations
• Perturbed rank 2 Poisson systems and periodic orbits on Casimir invariant manifolds