论文信息 - The Branch Locus for One-Dimensional Pisot Tiling Spaces

The Branch Locus for One-Dimensional Pisot Tiling Spaces

If phi is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Phi on the tiling space T_Phi factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Phi-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.

Richard Swanson | Marcy Barge | Beverly Diamond

[1] Boris Solomyak,et al. Pure Point Dynamical and Diffraction Spectra , 2002, 0910.4809.

[2] M. Barge,et al. Augmented dimension groups and ordered cohomology , 2009, Ergodic Theory and Dynamical Systems.

[3] J. Auslander,et al. Minimal flows and their extensions , 1988 .

[4] Marcy Barge,et al. Asymptotic orbits of primitive substitutions , 2003, Theor. Comput. Sci..

[5] Marcy Barge,et al. Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts , 2006 .

[6] M. Barge,et al. A complete invariant for the topology of one-dimensional substitution tiling spaces , 2001, Ergodic Theory and Dynamical Systems.

[7] F. M. Dekking,et al. The spectrum of dynamical systems arising from substitutions of constant length , 1978 .

[8] Marcy Barge,et al. Geometric theory of unimodular Pisot substitutions , 2006 .

[9] I. Putnam,et al. Topological invariants for substitution tilings and their associated $C^\ast$-algebras , 1998, Ergodic Theory and Dynamical Systems.

[10] Søren Eilers,et al. C *-algebras associated to dynamical systems , 2006 .

[11] S. Eilers,et al. Augmenting dimension group invariants for substitutional dynamical systems , 2006 .

[12] Søren Eilers,et al. Matsumoto $K$-groups associated to certain shift spaces , 2004, Documenta Mathematica.

[13] Proximality in Pisot tiling spaces , 2005, math/0509051.