1306.0923 (Mariusz Tarnopolski)

Bifurcation Diagrams and Generalized Bifurcation Diagrams for a rotational model of an oblate satellite    [PDF]

Mariusz Tarnopolski

This paper presents bifurcation and generalized bifurcation diagrams for a rotational model of an oblate satellite. Special attention is paid to parameter values describing one of Saturn's moons, Hyperion. For various oblateness the largest Lyapunov Characteristic Exponent (LCE) is plotted. The largest LCE in the initial condition as well as in the mixed parameter-initial condition space exhibits a fractal structure, for which the fractal dimension was calculated. It results from the bifurcation diagrams of which most of the parameter values for preselected initial conditions lead to chaotic rotation. The First Recurrence Time (FRT) diagram provides an explanation of the birth of chaos and the existence of quasi-periodic windows occuring in the bifurcation diagrams.

View original: http://arxiv.org/abs/1306.0923