Morphismes sturmiens et règles de Rauzy

Mignosi, Filippo; Séébold, Patrice

doi:10.5802/jtnb.91

Cited by 66 publications

(38 citation statements)

References 10 publications

(10 reference statements)

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“…In this paper, we show that in order to test whether a morphism f is Sturmian, it suffices to check whether the single word f(ba2ba2baba2bab) is balanced. This is in fact a strengthening of a result by Mignosi, Sddbold [14]. The decidability is an immediate consequence.…”

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confidence: 58%

A characterization of Sturmian morphisms

Berstel

Séébold

1993

Lecture Notes in Computer Science

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A morphism is Sturmiau if the image of every Sturmian word is a Sturmian word. Sturmian morphisms appear in number theory in connection with the so-called substitutions of characteristic sequences. A recent account of results in this direction is given by T. C. Brown in [4]. In this paper, we show that in order to test whether a morphism f is Sturmian, it suffices to check whether the single word f(ba2ba2baba2bab) is balanced. This is in fact a strengthening of a result by Mignosi, Sddbold [14]. The decidability is an immediate consequence. We also get a simpler proof of a theorem by Crisp et al. [5] characterizing those irrational numbers for which the characteristic sequence is a fixed point of a (Sturmian) morphism.* Partially supported by the PRC "Math~matiques et Informatique'.

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supporting

confidence: 58%

A characterization of Sturmian morphisms

Berstel

Séébold

1993

Lecture Notes in Computer Science

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“…65-68] where it is shown that [0;ç0)2i> • • •]> with the q % as below, is the simple continued fraction representing a of Définition 1 (see also [4] and a construction due to Rauzy [13,15] In the same way, Si and XiS % may be considered as infinité words on Ai -{X^Yi} (when useful, we précise the alphabet by writing "on A" or "G A^" or "G A*")-It follows also that if bfb (resp. ƒ6), ƒ G A*, is a factor (resp.…”

Section: : If S Is Proper Sturmian Then U G Fac(s) Implies U G Fac(s)mentioning

confidence: 99%

Decimations and sturmian words

Justin¹,

Pirillo²

1997

RAIRO-Theor. Inf. Appl.

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“…We mention some works related to symbolic dynamics of rotations: [HM40], [Hed44], [CH73], [Pau74], [BS94], [MS91]; this is but part of a long list of related papers.…”

Section: Introductionmentioning

confidence: 99%

The Scenery Flow for Geometric Structures on the Torus: The Linear Setting

Arnoux

Fisher²

2001

Chin. Annal Math.

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Abstract. We define the scenery flow of the torus. The flow space is the union of all flat 2-dimensional tori of area 1 with a marked direction (or equivalently, on the union of all tori with a quadratic differential of norm 1). This is a 5-dimensional space, and the flow acts by following individual points under an extremal deformation of the quadratic differential. We define associated horocycle and translation flows; the latter preserve each torus and are the horizontal and vertical flows of the corresponding quadratic differential.The scenery flow projects to the geodesic flow on the modular surface, and admits, for each orientation preserving hyperbolic toral automorphism, an invariant 3-dimensional subset on which it is the suspension flow of that map.We first give a simple algebraic definition in terms of the group of affine maps of the plane, and prove that the flow is Anosov. We give an explicit formula for the first-return map of the flow on convenient cross-sections. Then, in the main part of the paper, we give several different models for the flow and its cross-sections, in terms of:• stacking and rescaling periodic tilings of the plane;• symbolic dynamics: the natural extension of the recoding of Sturmian sequences, or the S-adic system generated by two substitutions; • zooming and subdividing quasi-periodic tilings of the real line, or aperiodic quasicrystals of minimal complexity; • the natural extension of two-dimensional continued fractions;• induction on exchanges of three intervals;• rescaling on pairs of transverse measure foliations on the torus, or the Teichmüller flow on the twice-punctured torus.

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Morphismes sturmiens et règles de Rauzy

Cited by 66 publications

References 10 publications

A characterization of Sturmian morphisms

A characterization of Sturmian morphisms

Decimations and sturmian words

The Scenery Flow for Geometric Structures on the Torus: The Linear Setting

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