Related papers: Necessary and sufficient conditions to be an eigen…
Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…
We prove measurable Livsic theorems for dynamical systems modelled by Markov Towers. Our regularity results apply to solutions of cohomological equations posed on Henon-like mappings and a wide variety of nonuniformly hyperbolic systems. We…
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…
If $(M,g)$ is a compact Riemannian manifold of dimension $n\ge 2$ we give necessary and sufficient conditions for improved $L^p(M)$-norms of eigenfunctions for all $2<p\ne p_c=\tfrac{2(n+1)}{n-1}$, the critical exponent. Since improved…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…
Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.
We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we…
We give elementary and explicit sufficient conditions (in particular, a functional correlation bound) for deterministic homogenisation (convergence to a stochastic differential equation) for discrete-time fast-slow systems of the form \[…
We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…
We consider various statements that characterize the hyperfinite II$_1$ factors amongst embeddable II$_1$ factors in the non-embeddable situation. In particular, we show that "generically" a II$_1$ factor has the Jung property (which states…
Renormalizations can be considered as building blocks of complex dynamical systems. This phenomenon has been widely studied for iterations of polynomials of one complex variable. Concerning non-polynomial hyperbolic rational maps, a recent…
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
Let $(X,\mu,T,d)$ be a metric measure-preserving dynamical system such that $3$-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence $(M_k)$ that converges to $0$ slowly enough, we obtain a strong…
In this article we consider a convex feasible set described by inequality constraints that are continuous and not necessarily Lipschitz or convex. We show that if the Slater constraint qualification and a non-degeneracy condition are…
We give necessary and sufficient conditions for existence and infinite divisibility of $\alpha$-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.
We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by…
We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion we construct new Markov rectangles such that their crossections by unstable…