scholarly journals A sofic system which is not spectrally of finite type

1988 ◽  
Vol 8 (3) ◽  
pp. 483-490 ◽  
Author(s):  
Susan Williams
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type ◽  
The Core ◽  
Sofic System ◽  
Core Matrix

AbstractWe exhibit a transitive sofic system for which the core matrix has negative trace, and hence cannot share the nonzero spectrum of any subshift of finite type cover. We also show that every transitive sofic system has an integral core matrix.

SPECTRA OF RECURRENCE DIMENSION FOR ADIC SYSTEMS

2002 ◽  
Vol 02 (04) ◽  
pp. 599-607 ◽  
Author(s):  
VÍCTOR F. SIRVENT
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type ◽  
Poincare Recurrence ◽  
Definition Of ◽  
Poincaré Recurrence

We compute the spectra of the recurrence dimension for adic systems and sub-adic systems. This dimension is characterized by the Poincaré recurrence of the system, and known in the literature as Afraimovich–Pesin dimension. These spectra are invariant under bi-Lipschitz transformations. We show that there is a duality between the spectra of an adic system and the corresponding subshift of finite type. We also consider Billingsley-like definition of the spectra of the recurrence dimension.

Recurrence in pairs

2008 ◽  
Vol 28 (4) ◽  
pp. 1135-1143 ◽  
Author(s):  
KAMEL HADDAD ◽  
WILLIAM OTT
Keyword(s):  
Finite Number ◽  
Finite Type ◽  
Sufficient Conditions ◽  
Dense Orbit ◽  
Subshift Of Finite Type

AbstractWe introduce and study the notion of weak product recurrence. Two sufficient conditions for this type of recurrence are established. We deduce that any point with a dense orbit in either the full one-sided shift on a finite number of symbols or a mixing subshift of finite type is weakly product recurrent. This observation implies that distality does not follow from weak product recurrence. We have therefore answered, in the negative, a question posed by Auslander and Furstenberg.

Prevalence of rapid mixing in hyperbolic flows

1998 ◽  
Vol 18 (5) ◽  
pp. 1097-1114 ◽  
Author(s):  
DMITRY DOLGOPYAT
Keyword(s):  
Finite Type ◽  
Periodic Orbits ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Suspension Flow ◽  
Subshift Of Finite Type ◽  
Rapid Mixing ◽  
Hyperbolic Flows ◽  
Necessary And Sufficient

We provide necessary and sufficient conditions for a suspension flow, over a subshift of finite type, to mix faster than any power of time. Then we show that these conditions are satisfied if the flow has two periodic orbits such that the ratio of the periods cannot be well approximated by rationals.

Languages, equicontinuity and attractors in cellular automata

1997 ◽  
Vol 17 (2) ◽  
pp. 417-433 ◽  
Author(s):  
PETR KŮRKA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
State Space ◽  
Finite Type ◽  
Measure Zero ◽  
Initial Conditions ◽  
The State ◽  
Subshift Of Finite Type ◽  
Topologically Transitive ◽  
The Third

We consider three related classifications of cellular automata: the first is based on the complexity of languages generated by clopen partitions of the state space, i.e. on the complexity of the factor subshifts; the second is based on the concept of equicontinuity and it is a modification of the classification introduced by Gilman [9]. The third one is based on the concept of attractors and it refines the classification introduced by Hurley [16]. We show relations between these classifications and give examples of cellular automata in the intersection classes. In particular, we show that every positively expansive cellular automaton is conjugate to a one-sided subshift of finite type and that every topologically transitive cellular automaton is sensitive to initial conditions. We also construct a cellular automaton with minimal quasi-attractor, whose basin has measure zero, answering a question raised in Hurley [16].

Conditions for topologically semi-conjugacy of the induced systems to the subshift of finite type

2017 ◽  
Vol 98 ◽  
pp. 1-6 ◽  
Author(s):  
Hyonhui Ju ◽  
Cholsan Kim ◽  
Yunmi Choe ◽  
Minghao Chen
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type

scholarly journals KMS STATES ON NICA–TOEPLITZ ALGEBRAS OF PRODUCT SYSTEMS

2012 ◽  
Vol 23 (12) ◽  
pp. 1250123 ◽  
Author(s):  
JEONG HEE HONG ◽  
NADIA S. LARSEN ◽  
WOJCIECH SZYMAŃSKI
Keyword(s):  
Finite Type ◽  
Lattice Ordered Group ◽  
Toeplitz Algebra ◽  
Product System ◽  
Natural Numbers ◽  
Ordered Group ◽  
Kms States ◽  
The Core ◽  
Product Systems ◽  
Affine Semigroup

We investigate KMS states of Fowler's Nica–Toeplitz algebra [Formula: see text] associated to a compactly aligned product system X over a semigroup P of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product system of finite type is introduced. If (G, P) is a lattice ordered group and X is a product system of finite type over P satisfying certain coherence properties, we construct KMSβ states of [Formula: see text] associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our results were motivated by, and generalize some of the results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers.

scholarly journals FINITELY CONSTRAINED GROUPS OF MAXIMAL HAUSDORFF DIMENSION

2015 ◽  
Vol 100 (1) ◽  
pp. 108-123 ◽  
Author(s):  
ANDREW PENLAND ◽  
ZORAN ŠUNIĆ
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Binary Tree ◽  
Rooted Tree ◽  
Finitely Generated ◽  
Subshift Of Finite Type ◽  
Regular Tree ◽  
Pattern Size ◽  
Tree Automorphisms ◽  
Pattern Group

We prove that if $G_{P}$ is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group $P$ of pattern size $d$, $d\geq 2$, and if $G_{P}$ has maximal Hausdorff dimension (equal to $1-1/2^{d-1}$), then $G_{P}$ is not topologically finitely generated. We describe precisely all essential pattern groups $P$ that yield finitely constrained groups with maximal Hausdorff dimension. For a given size $d$, $d\geq 2$, there are exactly $2^{d-1}$ such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree of depth $d$.

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