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The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…

The case of the planar circular restricted three-body problem where one of the two primaries is an oblate spheroid is investigated. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of…

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…

The main objective of this article is part of a research program to link the dynamics of fluid flows with the structure and its transitions in the physical spaces. As a prototype of problem and to demonstrate the main ideas, we study the…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…

This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…

We investigate the evolution of a system of colloidal particles, trapped at a fluid interface and interacting via capillary attraction, as function of the range of the capillary interaction and temperature. We address the collapse of an…

We study spin 3/2 fermionic cold atoms with attractive interactions confined in a one-dimensional optical lattice. Using numerical techniques, we determine the phase diagram for a generic density. For the chosen parameters, one-particle…

Cosmological simulations of dark matter structures have identified a set of universal profiles, and similar characteristics have been seen in non-cosmological simulations. It has therefore been speculated whether these profiles of…

For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we…

We use tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the…

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…

We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…

We evaluate masses of bottom and charmed baryons using several non-relativistic quark potentials which parameters have been adjusted to the meson spectra. Heavy Quark Symmetry leads to important simplifications of the three body problem,…

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system's evolution after deflection…

Based on the value of the orbital eccentricity of a particle and also its proximity to the exact resonant orbit in a three-body system, the Pendulum Approximation (Dermott & Murray 1983) or the Second Fundamental Model of Resonance (Andoyer…

Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…

In this paper we have examined numerically exact configurations of close binary systems composed of incompressible fluids with internal flows. Component stars of binary systems are assumed to be circularly orbiting each other but rotating…

The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is…

We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…