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We introduce a notion of minimal uniform attractor for nonautonomous random dynamical systems, which depends jointly on time and on a random parameter. Several examples are provided to illustrate the concept and to compare it with existing…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We prove the existence of recurrent initial configurations for the rotor walk on many graphs, including Z^d, and planar graphs with locally finite embeddings. We also prove that recurrence and transience of rotor walks are invariant under…
We consider a quite general problem concerning a linear free oscillation of a discrete mass-spring-damper system. This discrete sub-system is embedded into a one-dimensional continuum medium described by the linear telegraph equation. In a…
The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible…
There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
Consider $k\ge 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree $k$, and there is a very broad…
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…
We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability…
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
We investigate the (non)-existence of universal automata for some classes of automata, such as finite automata and pushdown automata, and in particular the influence of the representation and encoding function. An alternative approach,…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
In this note, we show how to provide sharp control on the least singular value of a certain translated linearization matrix arising in the study of the local universality of products of independent random matrices. This problem was first…
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…
The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…
In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given…