Extreme entropy versus growth rates of periodic orbits in equivalent flows (Q260551)

Two flows are called topologically equivalent if there exists a homeomorphism of their phase spaces that maps the orbits of one flow to the orbits of the other one and preserves the time orientation. It is known that two topologically equivalent flows without rest points have the same topological entropy and growth rate of the number of periodic orbits.NEWLINENEWLINEThe authors construct two topologically equivalent flows (with rest points) such that one flow has zero topological entropy and infinite growth rate of the number of periodic orbits while for the other one, these values are infinity and zero, respectively.