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Embedding tiling spaces in surfaces

100%

Holton C., Martensen B.

Fundamenta Mathematicae

2008

tom 201

nr 2

99-113

We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms in terms of asymptotic composants of substitutions.

Initial powers of Sturmian sequences

81%

Berthé V., Holton C., Zamboni L.

Acta Arithmetica

2006

tom 122

nr 4

315-347

Ograniczanie wyników

1 Acta Arithmetica

1 Fundamenta Mathematicae

2 Holton C.

1 Berthé V.

1 Martensen B.

1 Zamboni L.

1 2008

1 2006

Wyniki wyszukiwania

Embedding tiling spaces in surfaces

Initial powers of Sturmian sequences