17 research outputs found
Computer Algebra Solving of First Order ODEs Using Symmetry Methods
A set of Maple V R.3/4 computer algebra routines for the analytical solving
of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of
commands includes a 1st. order ODE-solver and routines for, among other things:
the explicit determination of the coefficients of the infinitesimal symmetry
generator; the construction of the most general invariant 1st. order ODE under
given symmetries; the determination of the canonical coordinates of the
underlying invariant group; and the testing of the returned results.Comment: 14 pages, LaTeX, submitted to Computer Physics Communications.
Soft-package (On-Line Help) and sample MapleV session available at:
http://dft.if.uerj.br/symbcomp.htm or ftp://dft.if.uerj.br/pdetool
Computer Algebra Solving of Second Order ODEs Using Symmetry Methods
An update of the ODEtools Maple package, for the analytical solving of 1st
and 2nd order ODEs using Lie group symmetry methods, is presented. The set of
routines includes an ODE-solver and user-level commands realizing most of the
relevant steps of the symmetry scheme. The package also includes commands for
testing the returned results, and for classifying 1st and 2nd order ODEs.Comment: 24 pages, LaTeX, Soft-package (On-Line help) and sample MapleV
sessions available at: http://dft.if.uerj.br/odetools.htm or
http://lie.uwaterloo.ca/odetools.ht
Fine-Tuning Solution for Hybrid Inflation in Dissipative Chaotic Dynamics
We study the presence of chaotic behavior in phase space in the
pre-inflationary stage of hybrid inflation models. This is closely related to
the problem of initial conditions associated to these inflationary type of
models. We then show how an expected dissipative dynamics of fields just before
the onset of inflation can solve or ease considerably the problem of initial
conditions, driving naturally the system towards inflation. The chaotic
behavior of the corresponding dynamical system is studied by the computation of
the fractal dimension of the boundary, in phase space, separating inflationary
from non-inflationary trajectories. The fractal dimension for this boundary is
determined as a function of the dissipation coefficients appearing in the
effective equations of motion for the fields.Comment: 10 pages, 4 eps figures (uses epsf), Revtex. Replaced with version to
match one in press Physical Review