Related papers: Manifold dynamics and orbital properties in a two-…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
We present two dimensional cylindrically symmetric hydrodynamic simulations and synthetic emission maps of a stellar wind propagating into an infalling, rotating environment. The resulting outflow morphology, collimation and stability…
We use our model for the formation and evolution of galaxies within a two-phase galaxy formation scenario, showing that the high-redshift domain typically supports the growth of spheroidal systems, whereas at low redshifts the predominant…
We present a new study of the evolution of the Carina dwarf galaxy that includes a simultaneous derivation of its orbit and star formation history. The structure of the galaxy is constrained through orbital parameters derived from the…
The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
We study the orbital structure in a series of self-consistent $N$-body configurations simulating rotating barred galaxies with spiral and ring structures. We perform frequency analysis in order to measure the angular and the radial…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Galaxy evolution reveals itself not only through the evolving properties of galaxies themselves but also through its impact on the surrounding environment. The intergalactic medium in particular holds a fossil record of past galaxy…
This chapter reviews theoretical work on the stellar dynamics of galaxy disks. All the known collective global instabilities are identified, and their mechanisms described in terms of local wave mechanics. A detailed discussion of warps and…
Using an energy balance model with ice sheets, we examine the climate response of an Earth-like planet orbiting a G dwarf star and experiencing large orbital and obliquity variations. We find that ice caps couple strongly to the orbital…
We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and…
This paper presents elements about the radial orbit instability, which occurs in spherical self-gravitating systems with a strong anisotropy in the radial velocity direction. It contains an overview on the history of radial orbit…
We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the…
We investigate the evolution of mass density profiles in secular disk galaxy models, paying special attention to the development of a two-component profile from a single initial exponential disk free of cosmological evolution (i.e., no…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related…
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from…
In the presence of a strong $m=2$ component in a rotating galaxy, the phase space structure near corotation is shaped to a large extent by the {\it invariant manifolds} of the short period family of unstable periodic orbits terminating at…