arXiv subjects

Pedro Henrique Barboza Rossetto

Publications and source records attributed to Pedro Henrique Barboza Rossetto.

3 recordsLinked to original sources

arXiv2026

Robust Wada Boundaries and Entropy Scaling in pp-Wave Spacetimes

We study the dynamics of the geodesics of pp-wave spacetimes with polynomial profiles, which are dynamically equivalent to the motion of a classical particle in a two-dimensional harmonic polynomial potential. We demonstrate that the Wada property of the escape basins is robust under variation of the polynomial degree, i.e., the basin boundaries remain maximally intermingled as the number of escape channels increases. We further provide a quantitative characterization of the degree of dynamical uncertainty by computing the basin entropy $S_{b}$ and the boundary basin entropy $S_{bb}$. We find that these measures increase monotonically with the polynomial degree, indicating enhanced unpredictability of the final state of the system. We also show that $S_{bb}$ is greater than $\ln(2)$ for $n>3$, and this confirms that the basin boundaries are fractal.

gr-qc↗

arXiv2024

Quadrupole Moment of a Magnetically Confined Mountain on an Accreting Neutron Star in General Relativity

General relativistic corrections are calculated for the quadrupole moment of a magnetically confined mountain on an accreting neutron star. The hydromagnetic structure of the mountain satisfies the general relativistic Grad-Shafranov equation supplemented by the flux-freezing condition of ideal magnetohydrodynamics, as in previous calculations of the magnetic dipole moment. It is found that the ellipticity and hence the gravitational wave strain are up to $12\%$ greater than in the analogous Newtonian system. The direct contribution of the magnetic field to the nonaxisymmetric component of the stress-energy tensor is shown to be negligible in accreting systems such as low-mass X-ray binaries.

astro-ph.HE↗

arXiv2023

Wada Boundaries on a Hyperbolic Pair of Pants

In this paper the geodesics of an open multiply connected hyperbolic manifold are presented from the dynamical system point of view. The approach is completely numerical. Similar to the closed hyperbolic case there is a zero-measure set of periodic orbits. The difference is that now, most of the geodesics escape to infinity through one of the topologically distinct channels, and initial conditions are identified to which channel the orbit escapes. The initial condition mesh reveals basins of attraction to each channel. We verified that the basin boundary points are of the Wada type by two independent methods. We have also calculated the basin entropy of the system, and verified that it depends on the opening angle of the escape channels. The manifold chosen is the pair of pants together with the leaves, so there are $3$ distinct exit channels.

nlin.CD↗