Related papers: Discrete Linear Canonical Evolution
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body…
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…
The dynamical realisation of the equation of state $p +\rho =0$ is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…
Using the example of the harmonic oscillator, we illustrate the use of hybrid dynamical brackets in analyzing quantum-classical interaction. We only assume that a hybrid dynamical bracket exists, is bilinear, and reduces to the pure…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model.…
The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify…
In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is essential and where the quantum model is…