UNBOUNDED NOT DIVERGING TRAJECTORIES IN MAPS WITH A VANISHING DENOMINATOR

To the memory of Professor Győrgy Targonski Abstract. Maps with a denominator which vanishes in a subset of the phase space may generate unbounded trajectories which are not divergent, i.e. trajectories invo­ lving arbitrarily large values of the dynamic variables but which are not attracted to infinity. In this paper we propose some simple one-dimensional and two-dimensional recurrences which generate unbounded chaotic sequences, and through these exam­ ples we try to explain the basic mechanisms and bifurcations leading to the creation of unbounded sets of attraction.