相关论文: Zero-one laws for eventually always hitting points…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
This paper defines and describes a few (related) notions of shrinking target property. We show that simultaneous expanding circle maps have a certain shrinking target property, but that circle homeomorphisms and isometries of complete,…
Geometrical objects with integral side lengths have fascinated mathematicians through the ages. We call a set $P=\{p_1,...,p_n\}\subset\mathbb{Z}^2$ a maximal integral point set over $\mathbb{Z}^2$ if all pairwise distances are integral and…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic…
We calculate the Hausdorff dimension of path-dependent shrinking target sets in generic affine iterated function systems. Here, by a path-dependent shrinking target set, we mean a set of points whose orbits infinitely often hit small balls…
We introduce the concepts of perpetual points and periodic perpetual loci in discrete--time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
We address the extreme value problem of a one-dimensional dynamical system approaching a fixed target while constrained to avoid a fixed set which can be thought of as a small hole. The presence of the latter influences the extremal index…
The quotient bases for zero-dimensional ideals are often of interest in the investigation of multivariate polynomial interpolation, algebraic coding theory, and computational molecular biology, etc. In this paper, we discuss the properties…
Recently, mass transference principles in metric number theory extend towards two direction. On one hand, the shape of the approximating sets can be taken of various shape, balls, rectangles or even general open sets (one refers to some…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
We study non-uniformly expanding maps of the unit interval with a parabolic fixed point at the origin that admit an ergodic absolutely continuous invariant measure, which may be finite or infinite. By introducing a hole defined by an…
Universal hitting sets are sets of words that are unavoidable: every long enough sequence is hit by the set (i.e., it contains a word from the set). There is a tight relationship between universal hitting sets and minimizers schemes, where…
We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb C^*=\mathbb C\setminus\{ 0\}$ for which both 0 and $\infty$ are essential singularities. Using annular covering lemmas we construct…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…
We describe, for the first time, a completely rigorous homotopy (path--following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial…