Williams' Decomposition Theorem, Shift-Flip Equivalence, and the Lind Zeta functions for Shift-Flip Systems of Finite Type
Sieye Ryu · arXiv (Cornell University) · 2014
Abstract. Shift-flip systems of finite type can be represented by a pair of zero-one square matrices, which is called a flip pair. The concepts of half elementary equivalence, strong shift-flip equivalence, and shift-flip equivalence between flip pairs are introduced. If two shift-flip systems of finite type are conjugate, then there is a sequence of an even number of half elementary equivalence between two flip pairs. If there is a strong shift-flip equivalence between two flip pairs, then there is a shift-flip equivalence between them and the Lind zeta functions for those shift-flip systems coincide. When there is a shift-flip equivalence between two flip pairs, the Lind zeta functions for those shift-flip systems may not coincide. When the Lind zeta functions for two shift-flip systems of finite type coincide, there may not exist a shift-flip equivalence between their flip pairs. 1.