Related papers: Spacetime diffeomorphisms and the geodesic approxi…

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism…

Cylindrically symmetric vacuum spacetimes are of immense interest in theoretical physics due to its connection to cosmic strings hypothesized in quantum field theory. In this article, we explore the properties of such spacetime and provide…

Geodesics deviation equation (GDE) is itroduced. In "adiabatic" approximation exact solution of the GDE if found. Perturbation theory in general case is formulated. Geometrical criterion of local instability which may lead to chaos is…

In this paper we describe the inelastic character of solitons of some slowly varying gKdV equations. We give precise lower bounds, in the energy space, of the defect induced by the potential on the solution as time goes to infinite. For the…

We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions…

A signature invariant geometric algebra framework for spacetime physics is formulated. By following the original idea of David Hestenes in the spacetime algebra of signature $(+,-,-,-)$, the techniques related to relative vector and…

We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…

A comprehensive account of a new structured algorithm for obtaining nonrelativistic diffeomorphism invariances in both space and spacetime by gauging the Galilean symmetry in a generic nonrelativistic field theoretical model is provided.…

I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…

We consider motion of a "magnetic'' soliton in two-component condensates along a non-uniform and time-dependent backgrounds in framework of the Hamiltonian mechanics. Our approach is based on generalization of Stokes' remark that soliton's…

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…

This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form.…

Localising the galileon symmetry along with Poincare symmetry we have found a version of galileon model coupled with curved spacetime which retains the internal galileon symmetry in covariant form. Also, the model has second order equations…

This short note is devoted to the Hamiltonian analysis of three dimensional gravity action that was proposed recently in [arXiv:1309.7231]. We modify given action in order to be invariant under non-relativistic diffeomorphism. Then we…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…

We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a…

The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force…

Diffeomorphisms can be seen as automorphisms of the algebra of functions. In the matrix regularization, functions on a smooth compact manifold are mapped to finite size matrices. We consider how diffeomorphisms act on the configuration…