Related papers: Topological entropy of generalized polygon exchang…
We prove that a polygonal billiard with one-sided mirrors has zero topological entropy. In certain cases we show sub exponential and for other polynomial estimates on the complexity.
We consider the billiard map in a convex polyhedron of $\mathbb{R}^3$, and we prove that it is of zero topological entropy.
We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
It is well-known that billiards in polygons cannot be chaotic (hyperbolic). Particularly Kolmogorov-Sinai entropy of any polygonal billiard is zero. We consider physical polygonal billiards where a moving particle is a hard disc rather than…
We show that a residual set of non-degenerate IETs on more than 3 letters is topologically mixing. This shows that there exists a uniquely ergodic topologically mixing IET. This is then applied to show that some billiard flows in a fixed…
We estimate from below the topological entropy of the generalized Bunimovich stadium billiards. We do it for long billiard tables, and find the limit of estimates as the length goes to infinity.
We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval…
We introduce the mean topological dimension for random bundle transformations, and show that continuous bundle random dynamical systems with finite topological entropy, or the small boundary property have zero mean topological dimensions.
In this note, we prove that every automorphism of a rational manifold which is obtained from $\Bbb{P}^k$ by a finite sequence blow-ups along smooth centers of dimension at most r with k>2r+2 has zero topological entropy.
We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…
In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table $\Bi := \bigcup_{n\in\N} [n,n+1] \times…
We study billiards in domains enclosed by circular polygons. These are closed $C^1$ strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories…
We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most…
We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
In this paper, we show that billiard orbits in rational polygons and geodesics on translation surfaces exhibit super-fast spreading, an optimal time-quantitative majority property about the corresponding linear flow that implies uniformity…
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…