The system spends long periods close to the bright periodic orbit, occasionally moving away for phases of chaotic dynamics that cover the rest of the attractor.
22.
"' Predrag Cvitanovi "'( born April 1, 1946 ) is a theoretical physicist regarded for his work in periodic orbit theory.
23.
"' Control of chaos "'is the stabilization, by means of small system perturbations, of one of these unstable periodic orbits.
24.
Does the " periodic orbits must be dense " bit need an equally intricate explanation ? talk ) 19 : 16, 17 September 2008 ( UTC)
25.
Once you've got a periodic orbit tidal forces can circularise it .-- talk ) 17 : 40, 11 July 2009 ( UTC)
26.
For other values of " a " and " b " the map may be chaotic, intermittent, or converge to a periodic orbit.
27.
After the information about the section has been gathered, one allows the system to run and waits until it comes near a desired periodic orbit in the section.
28.
If \ mathbf u _ 0 ( t ) is a known periodic orbit at a parameter value \ lambda _ 0 near \ lambda, then, Poincar?used
29.
In addition, a structurally stable system may have transversal homoclinic trajectories of hyperbolic saddle closed orbits and infinitely many periodic orbits, even though the phase space is compact.
30.
The image below shows a phase portrait before, at, and after a homoclinic bifurcation in 2D . The periodic orbit grows until it collides with the saddle point.
