Related papers: Inductive Rotation Tilings
We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our…
Here are two problems. First, understand the dynamics of a tiling billiard in a cyclic quadrilateral periodic tiling. Second, describe the topology of connected components of plane sections of a centrally symmetric subsurface $S \subset…
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous hulls resulting from these tilings are all topologically…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…
Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of…
Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and…
A tiling is said to have infinite local complexity (ILC) if it contains infinitely many two-tile patches up to rigid motions. In this work, we provide examples of substitution rules that generate tilings with ILC. The proof relies on…
We introduce rational Dyck tilings, or $(a,b)$-Dyck tilings, and study them by the decomposition into $(1,1)$-Dyck tilings. This decomposition allows us to make use of combinatorial models for $(1,1)$-Dyck tilings such as the Hermite…
In homotopy type theory, we construct the propositional truncation as a colimit, using only non-recursive higher inductive types (HITs). This is a first step towards reducing recursive HITs to non-recursive HITs. This construction gives a…
We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with a finite polysquare translation surface, and then modifying…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions. Their topological properties are fully encoded within a…
This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of the paper is an…
Given a collection of N rectangles such that the side ratio of each one is a quadratic irrationality, we find all rectangles which can be tiled by rectangles similar to one of the given ones. It means that each possible shape can be used…
Topological theories have established a new set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.