#
#Mon Aug 09 12:16:52 CEST 2010
Slide__KF8OUKOfEd-WfYQ0GneCwQ_subTitle=Cyclic motion of a system in two planes of the (at least three-dimensional) phase space generates a sort of <q>bike tube</q> as the attractor, i.e. a (two-dimensional) toroidal surface.  <p>On the <i>torus</i> attractor, exact periodicity is not guaranteed in general. However, after a long enough wait the (<i>quasiperiodic</i>) system returns arbitrarily often and arbitrarily close to each point of the torus surface (<i>recurrence</i>). Closely neighbouring trajectories do not depart from each other. If one only observes the system's behaviour long enough, one may forecast its motion for every desired timespan, it remains <i>predictable</i>.</p> <p>Imbedded in a <q>sea</q> of quasiperiodic orbits, though, lies even an infinite number of exactly periodic ones as well - namely those where minor and major revolutions exhibit integer mutual relationships.</p>
Slide__KF8OUKOfEd-WfYQ0GneCwQ_title=<p>Torus Attractor</p>
Slide__KF8OUKOfEd-WfYQ0GneCwQ_footer=<p>Source\: Vienna Technical University</p>