1.  Dynamical Systems and Chaos in Gravitation and in Inflationary Cosmologies

     In this line of research we study the general dynamics of inflationary models, as wel as universal statistical patterns
present in the its chaotic dynamics, and also study the structure of initial conditions given by Quantum Cosmology
for inflationary universes. We make use of dinamical structures as unstable periodic orbits present in the dynamics
of inflationary models that imply the existence of possible mechanisms of parametric ressonance amplification for
the formation of structures with a hierarchy of scales.

-Chaos and universality in the Dynamics of Inflationary Cosmologies,
Phys.Rev. D60, (Rapid Communications) 121301 (1999).

-Homoclinic Structure of Classical Spacetimes emerging from the Hartle-Hawking Model in Quantum Cosmology,
Phys.Rev. D60, 023512 (1999).

-Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models,
Modern Phys.Lett. A13, 1881-1886 (1998).
 

 2.  Topology Change in Quantum Gravity

Our aim here is to examine models in which quantum fluctuations of the geometry of the spacetime can lead to
topology change, and to answer the fascinating question whether the topology of the universe is given a priori or it
was fixed by quantum fluctuations of the geometry in the primordial universe. Theorems due to Geroch and Tipler
(1967, 1977) show that classicaly this change is forbidden. We calculated already concrete models in Quantum
Cosmology where topology change occurs [Phys.Rev. D56, 3329 (1997), gr-qc/0006096]. Extensions for more
complex configurations as black hole spacetimes are being implemented.
 

3.  General Dynamical Structures in Gravitational Collapse

We are presently applying methods used in the study of turbulence to try to establish the existence of general dynamical
structures in the gravitational collapse as, for instance, attractors and limit sets that allow us to distinguish in the
dynamics of collapsing gravitational configurations the ones that may form a black hole and the ones that are evanescent
to a flat spacetime.