Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve ${\mu }^2={\nu }^n-1,n\in \mathbb{Z}$: ergodicity, isochrony, periodicity and fractals

P. G. Grinevich, P. M. Santini

We study the complexification of the one-dimensional Newtonian particle in a monomial potential. We discuss two classes of motions on the associated Riemann surface: the rectilinea…