Related papers: One Dimensional p-adic Integral Value Transformati…
The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.
We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a…
Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant…
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
The stability theory of compact metric spaces with positive topological dimension is a well-established area in Dynamical Systems. A central result, attributed to Walters, connects the concepts of topological stability and the shadowing…
This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by…
In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
A Hamiltonian for a one-dimensional (1-D) dissipative system is given which shows that the trajectories in the spaces ($x,\dot x$) and ($x,p$) are completely different. The trajectory in the space ($x,p$) has an unexpected contra-intuitive…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
Let $\mathrm{SO}^+(p,q)$ denote the identity connected component of the real orthogonal group with signature $(p,q)$. We give a complete description of the spaces of continuous and generalized translation- and $\mathrm{SO}^+(p,q)$-invariant…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
A finite abelian $p$-group having an automorphism $x$ such that $1+\ldots+x^{p-1}=0$, can be viewed as a module over an appropriate discrete valuation ring $\mathcal{O}$ containing $\mathbb{Z}_p$ (the ring of $p$-adic integer). This yields…
In the preceding articles we considered fractional integral transforms involving one real scalar variable, one real matrix variable and real scalar multivariable case. In the present paper we consider the multivariable case when the…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
The author discusses integrability of Hamiltonian dynamical systems in the aftermath of KdV. The author also discusses the role of integrable systems in certain numerical computations, particularly the computation of the eigenvalues of a…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…