Furthermore, the non-wandering set of the system is precisely the union of singular points and periodic orbits.
12.
In the apparently periodic phases the behaviour is only nearly periodic, slowly drifting away from an unstable periodic orbit.
13.
At the bifurcation point the period of the periodic orbit has grown to infinity and it has become a homoclinic orbit.
14.
The intersection of the periodic orbit with the Poincar?section is a fixed point of the Poincar?map " F ".
15.
In another example, Feigenbaum period-doubling describes how a stable periodic orbit goes through a series of period-doubling bifurcations.
16.
The second comet found to have a periodic orbit was Encke's Comet ( with the official designation of 2P / Encke ).
17.
The stability of a periodic orbit of the original system is closely related to the stability of the fixed point of the corresponding Poincar?map.
18.
For example, the Ruelle & ndash; Takens scenario describes how a periodic orbit bifurcates into a torus and the torus into a strange attractor.
19.
The intersection of the disk with the given periodic orbit comes back to itself every period of the orbit and so do points in its neighborhood.
20.
The appearance or the disappearance of a periodic orbit through a local change in the stability properties of a steady point is known as the Hopf bifurcation.
