Related papers: Stability analysis of planetary systems via second…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
We systematically extend the statement that the configurational entropy provides an alternative approach to studying gravitational stability of compact objects, carried out in the previous work of M. Gleiser and N. Jiang, Phys. Rev. D {\bf…
R\'enyi entropy is a one-parameter generalization of Shannon entropy, which has been used in various fields of physics. Despite its wide applicability, the physical interpretations of the R\'enyi entropy are not widely known. In this paper,…
This work introduces a novel path-following control strategy inspired by the famous two-body problem, aiming to stabilize any Keplerian orbit. Utilizing insights from the mathematical structure of the two-body problem, we derive a robust…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…
We present a scheme for measuring R\'enyi entropies in generic atomic Hubbard and spin models using single copies of a quantum state and for partitions in arbitrary spatial dimension. Our approach is based on the generation of random…
Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for rapid and sometimes catastrophic shifts between them. The most common frameworks for analyzing stability changes, however, require…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
The Ricci curvature criterion is used for the investigation of the relative instability of several configurations of N-body gravitating systems. It is shown, that the systems with double massive centers are more unstable than the…
A restricted planar circular three-body system, consisting of the Sun and two planets, is studied as a simple model for a planetary system. The mass of the inner planet is considered to be larger and the system is assumed to be moving in a…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical…
We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different…
The R\'enyi entropies of Coulomb systems $R_{p}[\rho], 0 < p < \infty$ are logarithms of power functionals of the electron density $\rho(\vec{r})$ which quantify most appropriately the electron uncertainty and describe numerous physical…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
It has recently been stated that the warp structure observed around the star Beta Pictoris may be due to four planets embedded in its debris disk (Wahhaj et al., 2003). It, therefore, becomes important to investigate for what range of…
Thermodynamic stability of black holes, described by the R\'enyi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable…