Related papers: Independent resolutions for totally disconnected d…
We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at…
We examine the completely isometric automorphisms of a free product of noncommutative disc algebras. It will be established that such an automorphism is given simply by a completely isometric automorphism of each component of the free…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
We develop a $K$-theoretic approach to multiparameter bifurcation theory of homoclinic solutions of discrete non-autonomous dynamical systems from a branch of stationary solutions. As a byproduct we obtain a family index theorem for…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
We show that if any four distinct solutions of a rational difference equation are algebraically independent, then any number of distinct solutions to the equation are independent. A nontrivial variant of this result is given for autonomous…
We consider multidimensional differential systems (total differential systems and partial differential systems) with R-differentiable coefficients. We investigate the problem of the existence of R-holomorphic solutions, R-differentiable…
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…
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
We construct a nearest-neighbor Hamiltonian whose ground states encode the solutions to the NP-complete problem INDEPENDENT SET in cubic planar graphs. The Hamiltonian can be easily simulated by Ising interactions between adjacent particles…
We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…
Finite discrete-time dynamical systems (FDDS) model phenomena that evolve deterministically in discrete time. It is possible to define sum and product operations on these systems (disjoint union and direct product, respectively) giving a…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality and topological transitivity in the…
In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
We construct a ring of flows where we can decompose autonomous nonlinear dynamical systems into smaller parts, then solve each part and finally put everything together to obtain the exact solution of these systems.
The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…