Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown...

‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

Dynamical systems attract much attention due to their wide applications. Many significant results have been obtained in this field from various points of view. The present paper is devoted to an algebraic method of integration of three-dimensional nonlinear time dependent dynamical systems admitting nonlinear superposition with four-dimensional Vessiot-Guldberg-Lie algebras L4. The invariance o...