Related papers: Weyl Invariant Dynamics in 3 Dimensions

Estimates for invariant distances of convexifiable, $\C$-convexifiable and planar domains are given.

The invariants of the Thomas and the Weyl type for a mapping between non-symmetric affine connection spaces are obtained with respect to the factored deformation tensor in this paper. Motivated by two invariants of the Weyl type obtained in…

We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…

A manifestation of the three-body forces in multiparticle dynamics is discussed. The minireview of our recent results has been presented.

One of the key challenges in the dimension theory of smooth dynamical systems is in establishing whether or not the Hausdorff, lower and upper box dimensions coincide for invariant sets. For sets invariant under conformal dynamics, these…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the…

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are…

Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.

Certain aspects of nonrelativistic diffeomorphisms in 2+1 dimensions are investigated. These include a nonrelativistic limit of some relativistic actions in 3 dimensions, the Seiberg-Witten map, a modification of the viscosity tensor in…

An invariant of three-dimensional orientable manifolds is built on the base of a solution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.

The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…

The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…

Some aspects of the multidimensional soliton geometry are considered.

Given a polynomial P of partial derivatives of the Kahler metric, expressed as a linear combination of directed multigraphs, we prove a simple criterion in terms of the coefficients for $P$ to be an invariant polynomial, i.e. invariant…

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…

By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation…

We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…