Time-Dependent Attractor for the Oscillon Equation

Details Time-Dependent Attractor for the Oscillon Equation Time-Dependent Attractor for the Oscillon Equation

2010-09-13

arxiv.org/abs/1009.2529v1

Physics

Mathematical Physics

to appear in Discrete and Continuous Dynamical Systems

Scientific paper

We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of arbitrary polynomial growth. After constructing a suitable dynamical framework to deal with the explicit time dependence of the energy of the solution, we establish the existence of a regular, time-dependent global attractor. The sections of the attractor at given times have finite fractal dimension.

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