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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
DC Field | Value | Language |
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dc.contributor.advisor | 김영원 | - |
dc.contributor.author | 류시예 | - |
dc.date.accessioned | 2017-07-14T00:40:55Z | - |
dc.date.available | 2017-07-14T00:40:55Z | - |
dc.date.issued | 2014-02 | - |
dc.identifier.other | 000000018264 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121280 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2014. 2. 김영원. | - |
dc.description.abstract | 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. | - |
dc.description.tableofcontents | Abstract i
Introduction 1 Chapter 1. The Lind Zeta Function for Sofic Shift-Reversal Systems of Finite Order 7 1.1. Preliminaries: The Numbers of Periodic Points of Sofic Shifts 9 1.2. Automorphisms of Finite Order 16 1.3. Flip Systems 27 1.4. Reversals of Finite Order 39 1.5. N-Rationality 43 Chapter 2. Williams' Decomposition Theorem for Sofic Shift-Reversal Systems of Finite Order 49 2.1. Shift-Reversal Systems of Finite Order 50 2.2. Sofic-Shift Reversal Systems 55 2.3. Shift-Reversal Equivalence 59 Chapter 3. Krieger Presentations for Sofic Shift-Reversal Systems of Finite Order 63 3.1. Proofs of Proposition 1.3.7 and Proposition 1.4.4 66 3.2. Proof of Proposition 2.2.4 67 Bibliography 71 Abstract(in Korean) 73 Acknowledgement 75 | - |
dc.format | application/pdf | - |
dc.format.extent | 1306733 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Reversal maps | - |
dc.subject | Reversal systems | - |
dc.subject | Lind zeta functions | - |
dc.subject | Williams' decomposition theorem | - |
dc.subject.ddc | 510 | - |
dc.title | The Lind Zeta Function and Williams' Decomposition Theorem for Sofic Shift-Reversal Systems of Finite Order | - |
dc.title.alternative | 유한차 역행 소픽 기호 역학계에 대한 린드 제타함수와 윌리엄스 분해 정리 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Sieye Ryu | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 83 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2014-02 | - |
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