Related papers: Groups and nonlinear dynamical systems. Chaotic dy…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
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…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
A systematic study carried out on the infinite degeneracy and the constants of motion in the Landau problem establishes the central extension of the Euclidean group in two dimension as a dynamical symmetry group, and Sp(2,R) as spectrum…
In the paper we describe basin of attraction $p$-adic dynamical system $G(x)=(ax)^2(x+1)$. Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the $p$-adic…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from…
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…
We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $\beta$ functions of these theories are…
We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive…
In this note we consider the set of line operators in theories of class $S$. We show that this set carries the action of a natural discrete dynamical system associated with the BPS spectrum. We discuss several applications of this…
We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the…
Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables.…
The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law.…
The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the ladder…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
We demonstrate that the error dynamics of a thrusting spacecraft are nearly group affine on the $SE_2(3)$ Lie group, and the nonlinearity can be bounded, or removed with the application of a dynamic inversion control law. A numerical…
An SU(4) model of high-temperature superconductivity and antiferromagnetism has recently been proposed. The SO(5) group employed by Zhang is embedded in this SU(4) as a subgroup, suggesting a connection between our SU(4) model and the Zhang…