The branch locus for one-dimensional Pisot tiling spaces

• Autorzy: Marcy Barge , Beverly Diamond , Richard Swanson
• Języki publikacji: EN

Abstrakty

EN

If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space $𝓣_{Φ}$ factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.

Kategorie tematyczne

• 54H20: Topological dynamics
• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37B50: Multi-dimensional shifts of finite type, tiling dynamics
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 204
• Numer: 3
• Strony: 215-240

Daty

wydano

2009

Twórcy

autor

Marcy Barge

• Department of Mathematics, Montana State University, Bozeman, MT 59717, U.S.A.

autor

Beverly Diamond

• Department of Mathematics, College of Charleston, Charleston, SC 29424, U.S.A.

autor

Richard Swanson

• Department of Mathematics, Montana State University, Bozeman, MT 59717, U.S.A.

Identyfikatory

DOI

10.4064/fm204-3-2