Research Interests
Over the years research interests of course evolve.
Since I started doing
active research in the early seventies
I have worked on
the following topics
within the theory of dynamical systems
(going from recent to older):
As I find time I will try to add some comments to these topics;
I hope my co-authors will not be offended by the way they do or do not appear
in these (strictly personal) remarks.
-
A curious "change of stability without bifurcation" problem in laser physics.
A challenge posed to me by Sebius Doedel - I think I have a solution.
-
The "banana problem" in reversible systems.
- The continuation and bifurcation of periodic orbits in symmetric Hamiltonian
systems.
The emphasis is on methods which allow a more or less direct numerical implementation.
I am working on this in collaboration with Eusebius Doedel (Concordia University, Montréal, Canada)
and with Jorge Galán, Emilio Freire and Francisco-Javier Muñoz-Almaraz (Sevilla, Spain).
The methods which we have developped have been applied to several problems
from mechanics and physics;
in particular we are working on an extensive application
to the
3-body problem.
(By the way: the background picture which you see on this page originates from this research).
-
Persistence of quasi-periodic motions at 1:1-resonance in reversible systems.
-
Subharmonic bifurcation in reversible systems.
-
Generalized Lyapunov-Schmidt reduction techniques for periodic solutions of
differential equations and mappings.
-
Bifurcations of degenerate homoclinic orbits.
-
Period blow-up in reversible and Hamiltonian systems.
-
Center manifold theory.