## On g-functions for subshifts (2006)

Venue: | In Dynamics and Stochastics, IMS Lecture Notes-Monograph Series |

Citations: | 2 - 1 self |

### BibTeX

@INPROCEEDINGS{Krieger06ong-functions,

author = {Wolfgang Krieger},

title = {On g-functions for subshifts},

booktitle = {In Dynamics and Stochastics, IMS Lecture Notes-Monograph Series},

year = {2006}

}

### OpenURL

### Abstract

Abstract: A necessary and sufficient condition is given for a subshift presentation to have a continuous g-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous g-function. 1.

### Citations

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Citation Context ... its admissible words are defined by excluding finitely many words from appearing as subwords in them. Subshifts are studied in symbolic dynamics. For an introduction to symbolic dynamics see [7] and =-=[10]-=-. We introduce notation. Given a subshift X ⊂ Σ Z we set and We use similar notation also for blocks, x [i,k] = (xj)i≤j≤k, x ∈ X, i, k ∈ Z, i ≤ k, X [i,k] = {x [i,k] : x ∈ X}. b [i ′ ,k ′ ] = (bj)i ′ ... |

43 | Computational mechanics: Pattern and prediction, structure and simplicity
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Citation Context ...a subshift X ⊂ Σ Z the measure µ(x − ) ∈ M(Σ), or the inverse image under this mapping of a single measure, appear prominently within a theory that was put forward by James Crutchfield et al (see e.g.=-=[15]-=-). We set for a given transition complete and in-complete Shannon graph M ⊂ M(Σ) and for its accompanying measure λ-graph system λ-graph system ⋃ N∈Z+ MN inductively τa(µ) = τa−m(τa (−m,0] (µ)), 0 < m... |

39 |
Strongly mixing g-measures
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(Show Context)
Citation Context ...tions for subshifts 307 n∈N a ∈ X (−k,0], k ∈ Z+, {b ∈ X [1,n] : (x − , a, b) ∈ X (−∞,n]}, ω + n (a), a ∈ X (−k,0], k ∈ Z+. The notions of g-function and g-measure go back to Mike Keane’s papers [5], =-=[6]-=-. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],[14],[16],[17] and the references given there. For the origin of these ... |

20 |
Symbolic dynamics. Universitext
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(Show Context)
Citation Context ... type if its admissible words are defined by excluding finitely many words from appearing as subwords in them. Subshifts are studied in symbolic dynamics. For an introduction to symbolic dynamics see =-=[7]-=- and [10]. We introduce notation. Given a subshift X ⊂ Σ Z we set and We use similar notation also for blocks, x [i,k] = (xj)i≤j≤k, x ∈ X, i, k ∈ Z, i ≤ k, X [i,k] = {x [i,k] : x ∈ X}. b [i ′ ,k ′ ] =... |

16 |
des chaines a liaison complètes
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Citation Context ...substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],[14],[16],[17] and the references given there. For the origin of these notions see also =-=[2]-=-). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continuous g-functions and therefore introduce a g-function for a subshift X ⊂ Σ Z as a continuous mapp... |

15 |
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Citation Context ...The notions of g-function and g-measure go back to Mike Keane’s papers [5], [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. =-=[1]-=-,[4],[14],[16],[17] and the references given there. For the origin of these notions see also [2]). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continu... |

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Citation Context ...N ⊂ ⋃ N∈Z+ MN(Σ) where MN contains the probability vectors that are given by the marginals of the measures in M, and where the transition rules and the mapping ι are passed down from ⋃ N∈Z+ MN(Σ). In =-=[12]-=- Kengo Matsumoto introduced a class of structures that he called λ-graph systems. λ-graph systems have the form of a Bratteli diagram, that is, they have a finite number of vertices at each level. In ... |

13 |
Square summability of variations of g-functions and uniqueness of g-measures
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Citation Context ...notions of g-function and g-measure go back to Mike Keane’s papers [5], [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],=-=[4]-=-,[14],[16],[17] and the references given there. For the origin of these notions see also [2]). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continuous ... |

9 | Topological conjugacy for sofic systems. Ergodic Theory Dynam - Nasu - 1986 |

9 |
Multifractal analysis in symbolic dynamics and distribution of pointwise dimension for
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Citation Context ...ons of g-function and g-measure go back to Mike Keane’s papers [5], [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],=-=[14]-=-,[16],[17] and the references given there. For the origin of these notions see also [2]). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continuous g-fun... |

8 | graphs, subshifts and lambdagraph systems - Krieger, Matsumoto, et al. |

6 | Subsystems of finite type and semigroup invariants of subshifts, preprint - Hamachi, Inoue, et al. |

3 |
les mesures invariantes d’un recouvrement régulier, C.R.Acad.Sc.Paris 272
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Citation Context ...-functions for subshifts 307 n∈N a ∈ X (−k,0], k ∈ Z+, {b ∈ X [1,n] : (x − , a, b) ∈ X (−∞,n]}, ω + n (a), a ∈ X (−k,0], k ∈ Z+. The notions of g-function and g-measure go back to Mike Keane’s papers =-=[5]-=-, [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],[14],[16],[17] and the references given there. For the origin of t... |

3 |
On subshift presentations
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(Show Context)
Citation Context ...range in semi-infinite intervals. Recall that the n-block system of a subshift X ∈ ΣZ is its image in (X[1,n]) Z under the mapping x → (x(i,i+n])i∈Z, x ∈ X. Call a subshift X ⊂ ΣZ right instantaneous =-=[8]-=- if for all σ ∈ Σ, ω + 1 (σ) ̸= ∅.314 W. Krieger Proposition 4.1. A subshift X ⊂ Σ Z has a g-function if and only if one of its n-block systems is right-instantaneous. Proof. For n ∈ N and σ ∈ Σ one ... |

3 | à liaisons complètes et mesures de Gibbs unidimensionnelles, Thèse, Universite de Rouen - Maillard - 2003 |

3 |
Uniqueness in g-measures
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(Show Context)
Citation Context ...f g-function and g-measure go back to Mike Keane’s papers [5], [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],[14],=-=[16]-=-,[17] and the references given there. For the origin of these notions see also [2]). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continuous g-function... |

2 |
Regularity conditions and Bernoulli properties of equilibrium states and g-measures
- Walters
(Show Context)
Citation Context ...unction and g-measure go back to Mike Keane’s papers [5], [6]. Subsequently a substantial theory of g-functions and g-measures developed with contributions from many sides (see e.g. [1],[4],[14],[16],=-=[17]-=- and the references given there. For the origin of these notions see also [2]). These notions have formulations for general subshifts (see [11, p. 24]). We are interested in continuous g-functions and... |