Periodic orbits and their bifurcations in a 3-D system

Details Periodic orbits and their bifurcations in a 3-D system Periodic orbits and their bifurcations in a 3-D system

Jul 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..59..279c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 59, no. 3, p. 279-300

Mathematics

7

Astronomical Models, Branching (Mathematics), Mathematical Models, Orbit Calculation, Orbits, Stability, Uniqueness, Barred Galaxies, Classical Mechanics, Elliptical Galaxies, Hamiltonian Functions

Scientific paper

We study some simple periodic orbits and their bifurcations in the Hamiltonian (H = 1/2 ((x dot)2 + (y dot)2 + (z dot)2 + Ax2 + By2 + Cz2) - epsilon xz2 - eta yz2. We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (Delta). In the regions S and U there are lines of equal rotation number m/n. Along these lines we have bifurcations of families of periodic orbits of multiplicity n. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region Delta there are lines m/n, along which the orbits 1a, described n-times, are doubly unstable; however, along these lines there are no bifurcations of n-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (epsilon, eta). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams.

Affiliated with

Also associated with

No associations

Rating

Periodic orbits and their bifurcations in a 3-D system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Periodic orbits and their bifurcations in a 3-D system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodic orbits and their bifurcations in a 3-D system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1253644