Related papers: Dynamic general covariance of physical systems

The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…

A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…

We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…

We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…

The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…

We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…

We investigate gauge invariance against phase space shifting in nonequilibrium systems, as represented by time-dependent many-body Hamiltonians that drive an initial ensemble out of thermal equilibrium. The theory gives rise to gauge…

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…

One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…

This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…