  Instabilities and strong dynamical interactions between several giant planets
have been proposed as a possible explanation for the surprising orbital
properties of extrasolar planetary systems. In particular, dynamical
instabilities would seem to provide a natural mechanism for producing the
highly eccentric orbits seen in many systems. Here we present results from
numerical integrations for the dynamical evolution of planetary systems
containing two identical giant planets in nearly circular orbits very close to
the dynamical stability limit. We determine the statistical properties of the
three main types of systems resulting from the development of an instability:
systems containing one planet, following either a collision between the two
initial planets, or the ejection of one of them to infinity, and systems
containing two planets in a new, quasi-stable configuration. We discuss the
implications of our results for the formation and evolution of observed
extrasolar planetary systems. We conclude that the distributions of
eccentricities and semimajor axes for observed systems cannot be explained
easily by invoking dynamical interactions between two planets initially on
circular orbits. While highly eccentric orbits can be produced naturally by
these interactions, collisions between the two planets, which occur frequently
in the range of observed semimajor axes, would result in many more nearly
circular orbits than in the observed sample.
