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On sofic-like shifts and flips
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 김영원 | - |
| dc.contributor.author | 최혜경 | - |
| dc.date.accessioned | 2017-07-14T00:41:33Z | - |
| dc.date.available | 2017-07-14T00:41:33Z | - |
| dc.date.issued | 2015-08 | - |
| dc.identifier.other | 000000053341 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/121293 | - |
| dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2015. 8. 김영원. | - |
| dc.description.abstract | We study generalizations of the notion of sofic shifts and the existence of flips for a shift space.
Coded systems and almost sofic shifts generalize sofic shifts in terms of density of periodic points and entropies, respectively. An irreducible sofic shift is both coded and almost sofic. We investigate which properties of irreducible sofic shifts are extended to coded systems and almost sofic shifts. We also study which shift-flip systems have infinitely many non-conjugate flips. We prove that if an infinite synchronized system has a flip, then there are countably many non-conjugate flips. However, this property can not be extended to coded systems. We construct a coded system which has only two non-conjugate flips. | - |
| dc.description.tableofcontents | Abstract
1. Introduction 2. Preliminaries 2.1 Shift spaces 2.2 Sofic-like shifts 2.3 Flips for a shift space 3. Coded systems and almost sofic shifts 3.1 Characterizations of coded systems 3.2 Almost sofic shifts 4. Disk systems and their analogies 4.1 Construction of a disk system 4.2 Flips for the disk system $X(c, \alpha)$ 5. Some results of $S$-gap shifts and $\mathbf{X}(\xi, \xi', X)$ 5.1 The entropy and the zeta function of $S$-gap shifts 5.2 A synchronized system which is not periodic saturated 5.3 Some properties of $\mathbf{X}(\xi, \xi', X)$ 5.4 An almost sofic shift which is not periodic points dense 6. Shift-flip systems 6.1 Flips for a synchronized system 6.1.1 Proofs of Propositions 6.1.2 and 6.1.3 6.2 Flips for a certain coded system 6.3 Flips for the Morse shift | - |
| dc.format | application/pdf | - |
| dc.format.extent | 2275481 bytes | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | sofic shift | - |
| dc.subject | flip | - |
| dc.subject | coded system | - |
| dc.subject | almost sofic shift | - |
| dc.subject.ddc | 510 | - |
| dc.title | On sofic-like shifts and flips | - |
| dc.type | Thesis | - |
| dc.description.degree | Doctor | - |
| dc.citation.pages | iii, 102 | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2015-08 | - |
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