相关论文: Dynamical systems, celestial mechanics, and music:…

We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the…

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time…

A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting…

Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…

The changing heavens have played a central role in the scientific effort of astronomers for centuries. Galileo's synoptic observations of the moons of Jupiter and the phases of Venus starting in 1610, provided strong refutation of Ptolemaic…

Music has been called the temporal art par excellence. Yet, as this paper explains, it is also the atemporal art par excellence. The contradiction is, however, only apparent, and a result of viewing music from two possible perspectives.…

Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…

There may be structural principles pertaining to the general behavior of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to…

Since the 1960s a growing number of composers have engaged with scientific research and have tried to incorporate their understanding of various models and theories into their musical works. Among them, H\`ector Parra (b. 1976) has been…

Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…

These 1992 lectures notes present a powerful formalism mostly developed in the 1980s by Borderies, Goldreich and Tremaine to address planetary ring dynamical issues. These notes make a special emphasis on ring microphysics, quantified with…

A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…

We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…

We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular…

This paper describes a series of activities in which students investigate and use the Ptolemaic, Copernican, and Tychonic models of planetary motion. The activities guide students through using open source software to discover important…

The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…

We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a…

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in…

Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…

It has been speculated that gravity could be an emergent phenomenon, with classical general relativity as an effective, macroscopic theory, valid only for classical systems at large temporal and spatial scales. As in classical continuum…