Embedding tiling spaces in surfaces

• Autorzy: Charles Holton , Brian F. Martensen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37E35: Flows on surfaces
• 37C70: Attractors and repellers, topological structure
• 37B10: Symbolic dynamics
• 37B50: Multi-dimensional shifts of finite type, tiling dynamics
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 2
• Strony: 99-113

Daty

wydano

2008

Twórcy

autor

Charles Holton

• Department of Mathematics, The University of Texas at Austin, 1 University Station/C1200, Austin, TX 78712, U.S.A.

autor

Brian F. Martensen

• Minnesota State University, Wissink 273, Mankato, MN 56001, U.S.A.

Identyfikatory

DOI

10.4064/fm201-2-1