1,719 research outputs found
Stability properties and asymptotics for N non-minimally coupled scalar fields cosmology
We consider here the dynamics of some homogeneous and isotropic cosmological
models with interacting classical scalar fields non-minimally coupled to
the spacetime curvature, as an attempt to generalize some recent results
obtained for one and two scalar fields. We show that a Lyapunov function can be
constructed under certain conditions for a large class of models, suggesting
that chaotic behavior is ruled out for them. Typical solutions tend generically
to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic
results obtained for the one field model remain valid. In particular, we
confirm that, for large times and a vanishing cosmological constant, even in
the presence of the extra scalar fields, the universe tends to an infinite
diluted matter dominated era.Comment: 10 page
Stability of inflationary solutions driven by a changing dissipative fluid
In this paper the second Lyapunov method is used to study the stability of
the de Sitter phase of cosmic expansion when the source of the gravitational
field is a viscous fluid. Different inflationary scenarios related with
reheating and decay of mini-blackholes into radiation are investigated using an
effective fluid described by time--varying thermodynamical quantities.Comment: 17 pages, LaTeX 2.09, 2 figures. To be published in Classical and
Quantum Gravit
Chaotic dynamics in preheating after inflation
We study chaotic dynamics in preheating after inflation in which an inflaton
is coupled to another scalar field through an interaction
. We first estimate the size of the quasi-homogeneous
field at the beginning of reheating for large-field inflaton potentials
by evaluating the amplitude of the fluctuations on
scales larger than the Hubble radius at the end of inflation. Parametric
excitations of the field during preheating can give rise to chaos
between two dynamical scalar fields. For the quartic potential (,
) chaos actually occurs for in a
linear regime before which the backreaction of created particles becomes
important. This analysis is supported by several different criteria for the
existence of chaos. For the quadratic potential () the signature of chaos
is not found by the time at which the backreaction begins to work, similar to
the case of the quartic potential with .Comment: 12 pages, 10 figures, Version to appear in Classical and Quantum
Gravit
Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach
The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated
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