Are There Chaotic Tilings ?
نویسندگان
چکیده
We develop a class of examples in the form of tiling dynamical systems for use as toy models in statistical mechanics, to analyze the possible existence of disordered crystals. We give the first such models which are disordered in the sense of having no discrete spectrum. * Research supported in part by a grant from the Israel Science and Technology Ministry ** Research supported in part by NSF Grant No. DMS-9001475
منابع مشابه
Lattices of tilings and stability
Many tiling spaces such as domino tilings of fixed figures have an underlying lattice structure. This lattice structure corresponds to the dynamics induced by flips. In this paper, we further investigate the properties of these lattices of tilings. In particular, we point out a stability property: the set of all the shortest sequences of flips joining to fixed tilings also have a lattice struct...
متن کاملChaotic dynamical systems associated with tilings of RN
Chaos synchronization has exhibited an increasing interest in the last decade since the pioneering works reported in (Pecora & Carroll, 1990; Pecora & Carroll, 1991), and it has been advocated as a powerful tool in secure communication (Blekhman et al, 2002; Kolumban et al,1998; Nijmeijer, 1997; Kennedy & Ogorzalek, 1997). Chaotic systems are indeed characterized by a great sensitivity to the i...
متن کاملChaotic Attractors Near Forbidden Symmetry
We explore chaotic attractors with symmetries that are close to forbidden symmetries. In particular, attractors with planar crystallographic symmetry that contain an imperfect, but apparent, rotation that does not preserve the lattice of translations are constructed. This gives us a visual representation of patterns which have low symmetry type, but which contain additional, provocative structu...
متن کاملChaotic dynamical systems associated with tilings of R
In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of R , whose most familiar example is provided by the N−dimensional torus T . It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaossynchronization mechanis...
متن کاملTilings by Regular Polygons Iii: Dodecagon-dense Tilings
In Tilings and Patterns, Grünbaum and Shephard claim that there are only four kuniform tilings by regular polygons (for some k) that have a dodecagon incident at every vertex. In fact, there are many others. We show that the tilings that satisfy this requirement are either the uniform 4.6.12 tiling, or else fall into one of two infinite classes of such tilings. One of these infinite classes can...
متن کامل