Pure discrete spectrum in substitution tiling spaces
We introduce a procedure for establishing pure discrete spectrum for substitution tiling systems of Pisot family type and illustrate with several examples.
math.DS↗
arXiv subjects
M. Barge
Publications and source records attributed to M. Barge.
The Ingram Conjecture
We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of every two tent maps with different slopes in the interval [1, 2] are non-homeomorphic. Based on the structure obtained from the proof, we also show that every self-homeomorphism of the inverse limit space of the tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism.
math.DS↗