S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Ph.D. / Sc.D._수리과학부)
The Lind Zeta Function and Williams' Decomposition Theorem for Sofic Shift-Reversal Systems of Finite Order
유한차 역행 소픽 기호 역학계에 대한 린드 제타함수와 윌리엄스 분해 정리
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2014. 2. 김영원.
- We establish the Lind zeta function for automorphisms of shift spaces of finite order and introduce the generating function of shift-flip systems. A decomposition theorem for the Lind zeta function for reversal systems of finite order is established: we express it in terms of the Lind zeta function for automorphism and the generating functions of flip systems. In the sofic case, the Lind zeta function for reversal systems of finite order can be expressed in terms of matrices.
An analogue of Williams' decomposition theorem for reversal systems of finite order is established. To this end, we introduce the concept of half elementary conjugacy. Every conjugacy between two sofic shift-reversal systems of finite order can be decomposed into the composition of an even number of such half elementary conjugacies.