In the particular case of topological rank two subshifts, we prove their complexity is always subquadratic along a subsequence and their automorphism group is trivial. We also show that finite topological rank does not imply non-superlinear complexity. Now for each T-word W, I.tr(W °) ttsf (W °) will be a sum of boundedly many terms of the form (1.1). subshift of finite type of equal entropy onto T. A source for these is the survey article of Skau Sk. nonleading coefficients of the minimal polynomial of ,L Then, given another sofic shift T of equal entropy, there is a finite set E of positive integers such that the. This includes minimal Cantor systems given by Bratteli-Vershik representations whose tower levels have proportional heights and the so-called left to right S-adic subshifts. We also show that any minimal homeomorphism of the Cantor set is strongly orbit equivalent to one of zero entropy. When the complexity is non-superlinear, we prove that the automorphism group is, modulo a finite cyclic group, generated by a unique root of the shift. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. We model the dynamics of language shift as a competition process in which the numbers of speakers of each language (both monolingual and bilingual) vary as a function both of internal recruitment (as the net outcome of birth, death, immigration and emigration rates of native speakers), and of gains and losses owing to language shift. Conversely, we analyze the complexity of S-adic subshifts and provide sufficient conditions for a finite topological rank subshift to have a non-superlinear complexity. In this article we study automorphisms of Toeplitz subshifts. As an application, we show that minimal subshifts with non-superlinear complexity (like many classical zero-entropy examples) have finite topological rank. This is done by establishing necessary and sufficient conditions for a minimal subshift to be of finite topological rank. Minimal subshifts, Schtzenberger groups and profinite semigroups. We establish that such systems, when they are expansive, define the same class of systems, up to topological conjugacy, as primitive and recognizable S-adic subshifts. Updated MaBug fixes.Abstract : Minimal Cantor systems of finite topological rank (that can be represented by a Bratteli-Vershik diagram with a uniformly bounded number of vertices per level) are known to have dynamical rigidity properties. Updated MaNow supports saving search queries from PubMed and Google Scholar to We establish the equivalence of alpha -repulsive and alpha -finite for general subshifts over finite alphabets. My Folders! Look for the DeepDyve button next to your search results to add an article to a folder youĪs always, find the articles that are available to read on DeepDyve by looking for the orange 'available' In fact, if Xis subshift of nite type with positive topological entropy, then Xcontains a subshift which is not of nite type, and hence contains in nitely many. We prove that any 2-dimensional subshift of nite type can be characterized by a. Updated ApYou can now keep track of any article you find in PubMed or Google Scholar in Let X AZd be a 2-dimensional subshift of nite type. Updated ApUse DeepDyve to automatically keep track of what documents were interesting during your searches on PubMedĪnd Google Scholar! Find your combined document viewing history in the updated In some 'regular' cases, topological entropy can be computed by counting the number of distinct periodic orbits of period (and taking the upper limit after applying logarithm and dividing by ). Updated Bug fixes and performance improvements. For piecewise monotone interval maps, topological entropy is equal to the limit where denotes the number of pieces of monotonicity of. Updated See your Recent Activity directly from the popup!Īlso included: various bug fixes and improvements for automatically saving Recent Activity. We also obtained a quantitative upper bound for the measure of the spectrum. Updated Updating popup to properly display Science Direct searches and articles in your Recent Activity Updated Adding support for Science Direct searches and articles in your Recent Activity Updated Bug fixes and minor improvements to metadata collection for Recent Activity. Abstract: We show that the measure of the spectrum of Schr\'odinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the coupling constant tends to infinity.
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