arXiv subjects

Juan M. Aguirregabiria

Publications and source records attributed to Juan M. Aguirregabiria.

9 recordsLinked to original sources

arXiv2015

Simulating central forces in the classroom

We describe the easy to customize and extend open source Java program Central force workbench that can be used in the classroom to simulate the motion of a particle (or a two-body system) under central forces. It may be useful to illustrate problems in which the analytical solution is not available as well as to help students to grasp a more intuitive understanding of the main features of this kind of problem and to realize the exceptional nature of the particular case of Newtonian (and harmonic) forces. We also include some suggestions on how to use the program as a pedagogical tool.

physics.ed-ph↗

arXiv2014

Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero. Thus, the global vanishing previously found for the Schwarzschild metric remains linearly stable under slow rotational perturbations of this metric.

gr-qc↗

arXiv2010

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.

nlin.CD↗

arXiv2009

Robust chaos with prescribed natural invariant measure and Lyapunov exponent

We extend in several ways a recently proposed method to construct one-dimensional chaotic maps with exactly known natural invariant measure [Sogo 1999, 2009]. First, we assume that the given invariant measure depends on a continuous parameter and show how to construct maps with robust chaos --i.e., chaos that is not destroyed by arbitrarily small changes of the parameter-- and prescribed invariant measure and constant Lyapunov exponent. Then, by relaxing one condition in the approach of Refs. \cite{Sogo1,Sogo2}, we describe a method to construct robust chaos with prescribed constant invariant measure and varying Lyapunov exponent. Another extension of a condition in Refs. [Sogo 1999, 2009] provides a new method to get robust chaos with known varying Lyapunov exponent. In this third approach the invariant measure can be computed exactly in many particular cases. Finally we discuss how to use diffeomorphisms to construct maps with robust chaos, any number of parameters and prescribed invariant measure and Lyapunov exponent.

nlin.CD↗

arXiv2008

Robust chaos with variable Lyapunov exponent in smooth one-dimensional maps

We present several new easy ways of generating smooth one-dimensional maps displaying robust chaos, i.e., chaos for whole intervals of the parameter. Unlike what happens with previous methods, the Lyapunov exponent of the maps constructed here varies widely with the parameter. We show that the condition of negative Schwarzian derivative, which was used in previous works, is not a necessary condition for robust chaos. Finally we show that the maps constructed in previous works have always the Lyapunov exponent $\ln 2$ because they are conjugated to each other and to the tent map by means of smooth homeomorphisms. In the methods presented here, the maps have variable Lyapunov coefficients because they are conjugated through non-smooth homeomorphisms similar to Minkowski's question mark function.

nlin.CD↗

arXiv2005

Quintessence as k-essence

Quintessence and k-essence have been proposed as candidates for the dark energy component of the universe that would be responsible of the currently observed accelerated expansion. In this paper we investigate the degree of resemblance between those two theoretical setups, and find that every quintessence model can be viewed as a k-essence model generated by a kinetic linear function. In addition, we show the true effects of k-essence begin at second order in the expansion of the kinetic function in powers of the kinetic energy.

astro-ph↗

arXiv2004

Phantom k-essence cosmologies

We devise a method to obtain a phantom version of FRW k-essence cosmologies with homogeneous k-fields by applying form-invariance transformations. It can be seen that the transformation performs the maps $H\toH$ and $ρ+p\to-(ρ+p)$, which in turn give $γ\toγ$ and $a\to a^{-1}$. The discussion is presented in a general setup, valid for FRW k-essence cosmologies, and then we discuss power-law solutions for illustration purposes. First, we deal with models such that the gradient of the k-field is not constant, which include standard and generalized tachyon cosmologies. We concentrate on the usual tachyon and show the phantom symmetry involves a change in the potential and that it generates an extended super-accelerated tachyon field. Then, we turn our attention to models for which the time derivative of the k-field is not constant, and we show the transformation can be implemented without changing the potential at all.

astro-ph↗

arXiv2003

Symmetries leading to inflation

We present here the general transformation that leaves unchanged the form of the field equations for perfect fluid Friedmann--Robertson--Walker and Bianchi V cosmologies. The symmetries found can be used as algorithms for generating new cosmological models from existing ones. A particular case of the general transformation is used to illustrate the crucial role played by the number of scalar fields in the occurrence of inflation. Related to this, we also study the existence and stability of Bianchi V power law solutions.

gr-qc↗

arXiv1996

Chaotic scattering around black holes

It is shown that the scattering of a charged test particle by a system of four extreme Reissner-Nordtröm black holes is chaotic in some cases. The fractal structure of the scattering angle and time delay functions is another manifestation of the existence of a nonattracting chaotic set: fractal basin boundaries were previously known.

gr-qc↗