We call this sequence a dynamical system generated by f and denote by qj the value of q0 = q after j times of the map qj = f (q0). We encounter such systems in various occasion in mathematics, physics and in the nature. All of complex dynamical systems are examples in mathematics. Bäcklund transformations which characterize integrable systems, connection formulae of Stokes geometry E-mail: sait...

We consider a discrete-time non-Hamiltonian dynamics of quantum system consisting finite sample locally coupled to several bi-infinite reservoirs fermions with translation symmetry. In this setup, we compute the asymptotic state, mean fluxes into different reservoirs, as well entropy production rate dynamics. Formulas are explicitly expanded leading order in strength coupling reservoirs.

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

Abstract We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive master equations for the dynamics of the expected power in the discrete modes. In the case where the unperturbed dynamics has only discrete frequencies (finitely or infinitely many) the mode-power distribution is governed by an equation ...

The long-time behaviour of spectral semi-discretisations of weakly nonlinear wave equations is analysed. It is shown that the harmonic actions are approximately conserved also for the semi-discretised system. This permits to prove that the energy of the wave equation along the interpolated semi-discrete solution remains well conserved over long times and close to the Hamiltonian of the semi-dis...

In this article we derive the Marchenko integral equations for solving the inverse scattering problem for the matrix Zakharov-Shabat system with a potential without symmetry properties and having L1 entries under a technical hypothesis preventing the accumulation of discrete eigenvalues on the continuous spectrum. Wederive additional symmetry properties in the focusing case. The norming constan...

We analyze the (discrete) spectrum of the semirelativistic “spinless-Salpeter” Hamiltonian

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any...

Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...