Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Strange attractors in the Saturn ring system

The theory of deterministic chaos is used to study the three rings A, B, and C of Saturn and the French and Cassini divisions in between them. The data set comprises Voyager photopolarimeter measurements. The existence of spatially distributed strange attractors is shown, implying that the system is open, dissipative, nonequilibrium, and non-Markovian in character.