Related papers: Group Actions as Stroboscopic Maps of Ordinary Dif…
Discrete time dynamics on the SU(1,1) group is studied. It is shown that a map acting in the dual space is the stroboscopic map for a SU(1,1) Bloch equation. Exact solution of the map is used to elucidate the corresponding dynamics. It is…
An abstract Newton-like equation on a general Lie algebra is introduced such that orbits of the Lie-group action are attracting set. This equation generates the nonlinear dynamical system satisfied by the group parameters having an…
Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of…
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…
We study continuous 2-valued dynamical systems with discrete time (dynamics) on $\mathbb{C}$. The main question addressed is whether a 2-valued dynamics can be defined by the action of a 2-valued group. We construct a class of strongly…
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful…
In this paper a stochastic equation on compact groups in discrete negative time is studied. This is closely related to Tsirelson's stochastic differential equation, of which any solution is non-strong. How the group action reflects on the…
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…
In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
Discrete time (coined) quantum walks are produced by the repeated application of a constant unitary transformation to a quantum system. By recasting these walks into the setting of periodic perturbations to an otherwise freely evolving…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
We study group action on bimodules and bimodule categories and prove for them analogues of the results known for representations of skew group algebras, mainly in the case, when the action is separable.
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…