4/15/2023 0 Comments Sturmian subshift![]() Michal Kupsa (join work with tepn Starosta, published in 2015). because it happens to coincide with the Sturmian sequence. Let \(N^)\) has stronger forms of sensitivity if and only if \((X,f)\) has stronger forms of sensitivity, i.e. refinements/On factors of Sturmian subshifts. entropy minimal subshift on two symbols, generated by the kneading sequence. We show a slightly more general result which implies that these subshifts always exist in the case of groups of subexponential growth.Throughout this paper a topological dynamical system we mean a pair \((X,f)\), where X is a compact space and \(f:X\to X\) is a surjective continuous map. In this paper, we study these dynamical systems in more detail and compare their properties to the Sturmian case. Linearly recurrent subshifts have a finite number of non-periodic subshift factors Article Full-text available Aug 2008 ERGOD THEOR DYN SYST Fabien Durand View Show abstract Rotated odometers and. Moreover, we study the zeta-function of the spectral triple and relate its abscissa of convergence to the complexity exponent of the subshift or the. For repetitive tilings we show that if their patches have equi-distributed frequencies then the two metrics are Lipschitz equivalent. Also, it is known from Theorem 7 in 15 that there is a transitive and sensitive subshift, which is not syndetically sensitive. For Sturmian subshifts this is equivalent to linear recurrence. In our earlier work, we introduced another type of subshift of optimal squareful words which together with the square root map form a dynamical system. From Corollary 3 and Theorem 5 in 15, it follows that every Sturmian subshift is syndetically sensitive, but no Sturmian subshift is cofinitely sensitive. The dynamics of the square root map on a Sturmian subshift are well understood. A direct consequence of this result is that every countable group has a strongly aperiodic subshift on the alphabet has uniform density α ∈ \alpha \in α ∈ if for every configuration the density of 1's in any increasing sequence of balls converges to α \alpha α. The dynamics of the square root map on a Sturmian subshift are well understood. We show that there is a large class of numbers ( 0, 1 ) such that the subshift with parameter has finite Connes metric and induces the weak. Moreover, we study the zeta-function of the spectral triple and relate its abscissa of convergence to the complexity exponent of the subshift or the tiling. A theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a 2-coloring. For Sturmian subshifts, the results depend rather subtly (but probably not surprisingly) on the continued fraction expansion of the irrational number which parameterizes the subshift. For Sturmian subshifts this is equivalent to linear recurrence. ![]()
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