Studies of the Hoyer system

摘要

We study a three-dimensional dynamical system depending on nine parameters-the so-called Hoyer system. The aim is to find the values of parameters for which this system has a Poisson structure with a quadratic Hamiltonian. We show that there exist four families of Poisson structures. In more detail, we study the case when the system admits a family of different structures for a fixed Hamiltonian.