Related papers: Cone structures from a dynamical and probabilistic…
This paper employs an alternate dynamical model of the circular restricted three body problem to quantify uncertainties associated with spacecraft thrusting maneuvers. A non-product quadrature scheme known as Conjugate Unscented Transform…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
This study investigates the exact geometry of the configuration space in three-dimensional rotational motion planning. A parameterization of configuration space obstacles is derived for a given triangulated or ball-approximated scene with…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower…
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…
The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate…
In the preliminary design of space missions it can be useful to identify regions of dynamics that drive the system's behaviour or separate qualitatively different dynamics. The Lagrangian Coherent Structure (LCS) has been widely used in the…
[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes…
To better understand the orbital dynamics of exoplanets around close binary stars, i.e., circumbinary planets (CBPs), we applied techniques from dynamical systems theory to a physically motivated set of solutions in the Circular Restricted…
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
This paper introduces the Circular Restricted n-Body Problem (CRNBP), an extension of the bicircular restricted four-body problem (BCR4BP) designed to describe the dynamics of an n-body system. In the CRNBP, each massive body in the system…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on…