A blackboard of Lord Robert May (1972), presenting the period doubling scenario.
Nonlinear 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 4D Poincare' crosssections. 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 twocomponent galactic potential''.
Astronomy & Astrophysics 227, 3748 (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 4dimensional 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
