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\title{New findings on Perlick system I: \\ from the algebra of symmetries to
the geometry of the orbits}
\author{O. Ragnisco \\
Instituto Nazionale di Fisica Nucleare, Sezione di Roma 3 \\Via della Vasca Navale 84, 00146 Roma, Italy }
\date{}
\maketitle
We investigate the main algebraic properties of the maximally superintegrable
system known as ``Perlick system type I'', by using a classical variant of the
so called factorization method. As it is expected for maximally superintegrable
systems, the algebraic structure sheds light also on the geometric features of
the trajectories. The crucial role played by the rational parameter $\beta$
will be seen ``in action''.
\begin{thebibliography}{1}
\bibitem[1]{key-1} \c{S}. Kuru, J. Negro and O. Ragnisco, \emph{The Perlick
system type I: from the algebra of symmetries to the geometry of the
trajectories}, arXiv:1705.04618v1
\end{thebibliography}
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