Related papers: Torus mapper: a code for dynamical models of galax…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
We propose DeepExplorer, a simple and lightweight metric-free exploration method for topological mapping of unknown environments. It performs task and motion planning (TAMP) entirely in image feature space. The task planner is a recurrent…
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…
The structure of interstellar medium can be characterised at large scales in terms of its global statistics (e.g. power spectra) and at small scales by the properties of individual cores. Interest has been increasing in structures at…
We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the…
In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic copies of the torus such that the motion on them is conjugated…
Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a…
In this paper we present a procedure to compute reducible invariant tori and their stable and unstable manifolds in stroboscopic Poincar\'e maps. The method has two steps. In the first step we compute, by means of a quadratically convergent…
Understanding oscillations and waves in astrophysical fluid bodies helps to elucidate their observed variability and the underlying physical mechanisms. Indeed, global oscillations and bending modes of accretion discs or tori may be…
We use Laskar's frequency mapping technique to study the dynamics of triaxial galaxies with central density cusps and nuclear black holes. For ensembles of 10^4 orbits, we numerically compute the three fundamental frequencies of the motion,…
Solar tomography has progressed rapidly in recent years thanks to the development of robust algorithms and the availability of more powerful computers. It can today provide crucial insights in solving issues related to the line-of-sight…
Emission and absorption line features are important diagnostics for the physics underlying extragalactic astronomy. The interpretation of observed signatures involves comparing against forward modeled spectra from galaxy formation…
We present POLAR, a polynomial arithmetic-based framework for efficient bounded-time reachability analysis of neural-network controlled systems (NNCSs). Existing approaches that leverage the standard Taylor Model (TM) arithmetic for…
We show here how, using Euler's integration method and an associated function bounding the error in function of time, one can generate structures closely surrounding the invariant tori of dynamical systems. Such structures are constructed…
We investigate the structure of galaxies formed in a suite of high-resolution cosmological simulations. Consistent with observations of high-redshift galaxies, our simulated galaxies show irregular, prolate shapes, which are dominated by…
Close-in exoplanets with H/He atmospheres often undergo hydrodynamic escape. In extreme cases, it is hypothesized that the mass loss can be high enough for the escaping planetary material to wrap around the star, forming a long-lasting…
We numerically explore on galaxy scales the Dipolar dark matter (DM) model based on the concept of gravitational polarization. This DM model has been proposed as a natural way to reproduce observed tight galactic scaling relations such as…
Numerical N-body simulations are commonly used to explore stability regions around exoplanets, offering insights into the possible existence of satellites and ring systems. This study aims to utilize Machine Learning (ML) techniques to…
We consider autonomous Hamiltonian systems and present an algorithm to compute at the same time partially hyperbolic invariant tori (whiskered tori), as well as high-order expansions of their stable and unstable manifolds. Such whiskered…
We present a KAM theorem for presymplectic dynamical systems. The theorem has a " a posteriori " format. We show that given a Diophantine frequency $\omega$ and a family of presymplectic mappings, if we find an embedded torus which is…