Related papers: Park--Tarter Matrix for a Dyon--Dyon System
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function,…
In this paper we investigate the problem of linearizability for a family of cubic complex planar systems of ordinary differential equations. We give a classification of linearizable systems in the family obtaining conditions for…
This article deals with nonrelativistic study of a D-dimensional superintegrable system, which generalizes the ordinary isotropic oscillator system. The coefficients for the expansion between the hyperspherical and Cartesian bases…
In this paper, we give a direct method to study the isochronous centers on center manifolds of three dimensional polynomial differential systems. Firstly, the isochronous constants of the three dimensional system are defined and its…
It is shown that the three-dimensional isotropic oscillator with coordinates belonging to the two-dimensional half-up cone is dual to the cyon , i.e. the planar particle-vortex bound system provided by fractional statistics.
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
In this paper, we consider linear boundary port-Hamiltonian distributed parameter systems on a time-varying spatial domain. We derive the specific time-varying Dirac structure that these systems give rise to and use it to formally establish…
The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents…
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector…
We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets…
We present a simple description of pion-nucleon ($\pi N$) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this we solve Dyson-Schwinger equations within the framework of Time-Ordered…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…
We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…