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

摘要

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