Computer Science
Scientific paper
Dec 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994ijbc....4.1399p&link_type=abstract
INTERNATIONAL JOURNAL of BIFURCATION and CHAOS, VOL.4, No. 6, 1399-1424
Computer Science
1
Complex Instability, Triaxial Systems, Periodic Orbits
Scientific paper
The problems encountered in the study of 3-dimensional Hamiltonian systems by means of the Poincare cross-sections are reviewed. A new method to overcome these problems is proposed. In order to visualize the four-dimensional "space" of section it is introduced the use of color and rotation. We apply this method to the case of a family of simple periodic orbits in a 3-dimensional potential and we describe the differences in the orbital behavior between regions close to stable and unstable periodic orbits. We outline the differences between the transition from stability to simple instability and the transition from stability to complex instability. We study the changes in the structure of the 4D "spaces" of section, which occur when the family becomes complex unstable and we conclude that the orbital behavior after the transition depends on the orbital behavior before it.
Patsis Panos A.
Zachilas L.
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