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Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
We determine the autonomous three dimensional Newtonian systems which admit Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian systems, which admit Noether point symmetries. We apply the results in order to…
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
In this paper we use a dynamical approach to prove some new divergence theorems on complete non-compact Riemannian manifolds.
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…
We first consider the Hamiltonian formulation of $n=3$ systems in general and show that all dynamical systems in ${\mathbb R}^3$ are bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. We…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…