A blackboard of Lord Robert May (1972), presenting the period doubling scenario.
Non-linear Phenomena like Complex Instability, Inverse Bifurcations and Collisions of Bifurcations have been investigated in triaxial Hamiltonian systems. The models represent a thick disk (modified Miyamoto potential) embedded in a triaxial logarithmic halo. Parameters are chosen to match the potential of the Milky Way.

Furthermore a method using colors and rotation has been proposed for visualizing 4-D Poincare' cross-sections. As an application the structure of the "spaces of section" after a transition from stability to (simple, double or complex) instability has been studied.

Work on 3D Hamiltonian systems has been done together with L. Zachilas (University of Thessalia Greece) (see references below).

The visualization of the 4D Poincare space of section close to a Simple Unstable periodic orbit using the method proposed by Patsis and Zachilas (1994). The b/w diagram (left) is given for comparison with the corresponding rotated color figure (right).

References:

• P.A. Patsis and L. Zachilas: ``Complex instability of simple periodic orbits in a realistic galactic potential'' in ``Le monde des galaxies'', H.G Corwin and L. Botinelli (eds.) Springer 1988
• P.A. Patsis and L. Zachilas: ``Complex instability of simple periodic orbits in a realistic two-component galactic potential''. Astronomy & Astrophysics 227, 37-48 (1990)
• P.A. Patsis and L. Zachilas: ``A method for visualizing the 4D space of section in a 3D Hamiltonian system'' in ``Hamiltonian Mechanics'' (NATO's ASI) J. Seimenis (ed), Plenum Press N.Y., 1994, pg. 399
• P.A. Patsis and L. Zachilas: ``Using color and rotation for visualizing 4-dimensional Poincare' Cross sections'' I.J. of Bif. and Chaos, Vol4, No6 (1994) 1399.
• Patsis, P. A.; Efthymiopoulos, C.; Contopoulos, G.; Voglis, N. Dynamical spectra of barred galaxies. 1997 A&A...326..493