Related papers: Linear Fractional p-Adic and Adelic Dynamical Syst…

In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in…

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…

Let X be a smooth curve defined over the algebraic numbers, let a,b be algebraic numbers, and let f_l(x) be an algebraic family of rational maps indexed by all l in X. We study whether there exist infinitely many l in X such that both a and…

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with nite local complexity the only equicontinuous systems are then shown to be…

We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…

Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…

We explicitly give all stationary solutions to the focusing cubic NLS on the line, in the presence of a defect of the type Dirac's delta or delta prime. The models proves interesting for two features: first, they are exactly solvable and…

For a class of groups $G$ over a field $\mathbb{F}$, including certain Lie groups, Algebraic groups and finite groups, we develop a general method to determine rational and real elements, thereby unifying earlier group-specific results into…

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely…

We study the theory of finite-order p-adic functions and distributions on ray class groups of number fields, and apply this to the construction of (possibly unbounded) p-adic L-functions for automorphic forms on GL(2) which may be…

Let $K$ be a global function field of characteristic $p$ and degree $D$ over $\mathbb F_{p}(t)$. We consider dynamical systems over the projective line $\mathbb P^1(K)$ defined by rational maps with at most one prime of bad reduction. The…

With respect to the analytic-algebraic dichotomy, the theory of Siegel modular forms of half-integral weight is lopsided; the analytic theory is strong whereas the algebraic lags behind. In this paper, we capitalise on this to establish the…

The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…

In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…

We study some subsets of rational points in an algebraic groups defined by open conditions on their projection in the finite adeles points. Using adelic mixing we are able to prove an equidistribution's result for the projection of these…

Let $\sigma$ denote an endomorphism of a smooth algebraic group $G$ over the algebraic closure of a finite field, and assume all iterates of $\sigma$ have finitely many fixed points. Steinberg gave a formula for the number of fixed points…

Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…