Newtonian vs. relativistic chaotic scattering

It is shown that Newtonian mechanics is not appropriate to compute approximate individual trajectories with small velocities in chaotic scattering. However, some global properties of the dynamical system, such as the dimension of the non-attracting chaotic invariant set, are more robust and the Newtonian approximation provides reasonably accurate results for them in slow chaotic scattering.Comment: 2 pages, 2 figures

Order reductions of Lorentz-Dirac-like equations

We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure

Tracking solutions in tachyon cosmology

We perform a thorough phase-plane analysis of the flow defined by the equations of motion of a FRW universe filled with a tachyonic fluid plus a barotropic one. The tachyon potential is assumed to be of inverse square form, thus allowing for a two-dimensional autonomous system of equations. The Friedmann constraint, combined with a convenient choice of coordinates, renders the physical state compact. We find the fixed-point solutions, and discuss whether they represent attractors or not. The way the two fluids contribute at late-times to the fractional energy density depends on how fast the barotropic fluid redshifts. If it does it fast enough, the tachyonic fluid takes over at late times, but if the opposite happens, the situation will not be completely dominated by the barotropic fluid; instead there will be a residual non-negligible contribution from the tachyon subject to restrictions coming from nucleosynthesis.Comment: 5 pages, 4 figure

Regular order reductions of ordinary and delay-differential equations

We present a C program to compute by successive approximations the regular order reduction of a large class of ordinary differential equations, which includes evolution equations in electrodynamics and gravitation. The code may also find the regular order reduction of delay-differential equations.Comment: 4 figure