Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Van Cyr"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 3 (2015)
For a finite alphabet ${\mathcal{A}}$ and shift $X\subseteq {\mathcal{A}}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group $\text{Aut}(X)$. For such systems, we show th
Externí odkaz:
https://doaj.org/article/3bd81a36ef4b4978b84831b607ff5adb
Autor:
VAN CYR
Publikováno v:
Proceedings of the American Mathematical Society, 2012 Sep 01. 140(9), 3035-3040.
Externí odkaz:
http://dx.doi.org/10.1090/S0002-9939-2012-11258-4
Autor:
Vaughn Climenhaga, Van Cyr
Publikováno v:
Israel Journal of Mathematics. 232:899-920
For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological entropy. We giv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e2c14f5a95bb7c6f1531e3d354d6821
https://doi.org/10.1007/s11856-019-1891-5
https://doi.org/10.1007/s11856-019-1891-5
We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily from a classical result of Parry that the full shift on finitely many
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b550727254a41246f80ffe98efa964f
Publikováno v:
Journal of modern dynamics
Journal of modern dynamics, American Institute of Mathematical Sciences, 2018, 13 (1), pp.147-161. ⟨10.3934/jmd.2018015⟩
Journal of modern dynamics, American Institute of Mathematical Sciences, 2018, 13 (1), pp.147-161. ⟨10.3934/jmd.2018015⟩
The set of automorphisms of a one-dimensional subshift \begin{document} $(X, σ)$ \end{document} forms a countable, but often very complicated, group. For zero entropy shifts, it has recently been shown that the automorphism group is more tame. We pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7817387c3247249e4480ce1bf799e23a
https://doi.org/10.3934/jmd.2018015
https://doi.org/10.3934/jmd.2018015
A subshift with linear block complexity has at most countably many ergodic measures, and we continue the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity is arbitrarily
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c44f478ecdc590db448dd62ae244c1d3
http://arxiv.org/abs/1902.08645
http://arxiv.org/abs/1902.08645
Publikováno v:
Journal of Modern Dynamics. 10:483-495
The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a569d56b1cd7768bcd7752bd3ab23aee
https://doi.org/10.3934/jmd.2016.10.483
https://doi.org/10.3934/jmd.2016.10.483
Publikováno v:
Proceedings of the American Mathematical Society. 145:1163-1173
Using results relating the complexity of a two dimensional subshift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on [ 0 , 1 ) [0,1) which is invariant under both x ↦ p x ( m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::69daec94dda4a02d9df4c543b6a8878a
https://doi.org/10.1090/proc/13279
https://doi.org/10.1090/proc/13279
Publikováno v:
European Journal of Combinatorics. 52:146-173
The Morse-Hedlund Theorem states that a bi-infinite sequence $\eta$ in a finite alphabet is periodic if and only if there exists $n\in\N$ such that the block complexity function $P_\eta(n)$ satisfies $P_\eta(n)\leq n$. In dimension two, Nivat conject
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3b074b262b5c6e6575861e2085993b1a
https://doi.org/10.1016/j.ejc.2015.10.003
https://doi.org/10.1016/j.ejc.2015.10.003
Publikováno v:
Proceedings of the American Mathematical Society. 144:613-621
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to be large f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6783d480847d6f85b83e31873794b6c
https://doi.org/10.1090/proc12719
https://doi.org/10.1090/proc12719