TWO NEW SOLVABLE DYNAMICAL SYSTEMS OF GOLDFISH TYPE

Abstract

Two new solvable dynamical systems of goldfish type are identified, as well as their isochronous variants. The equilibrium configurations of these isochronous variants are simply related to the zeros of appropriate Laguerre and Jacobi polynomials.

Keywords:

• Integrable dynamical systems
• solvable many-body problems
• isochronous systems
• zeros of classical polynomials
• dynamical systems of goldfish type