DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Shin, Su-Jin | - |
dc.contributor.advisor | 신수진 | - |
dc.contributor.author | Jung, Ui-Jin | - |
dc.contributor.author | 정의진 | - |
dc.date.accessioned | 2011-12-14T04:40:39Z | - |
dc.date.available | 2011-12-14T04:40:39Z | - |
dc.date.issued | 2009 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=327747&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41927 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2009. 8., [ iii, 82 p. ] | - |
dc.description.abstract | We study the topological and dynamical properties of sliding block codes between shift spaces together with the existence and extensions of these codes. Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions ─ open, constant-to-one, (right or left) closing ─ imply the third. If the range is not sofic, then the same result holds when bi-closingness replaces closingness. Properties of open mappings between shift spaces are investigated in detail. In Chapter 3, properties of infinite-to-one codes are given. For an almost specified shift X, we show that an irreducible shift of finite type Y of lower entropy is a factor of X if and only if it is a factor of X by an open bi-continuing code. If these equivalent conditions hold and Y is mixing, then any code from a proper subshift of X to Y can be extended to an open bi-continuing code on X. In Chapter 4, we find a connection between symbolic dynamics and graph theory. Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We give several sufficient conditions for a bi-resolving homomorphism to have a bi-covering extension with an irreducible domain. Using these results, we prove that a bi-closing code between subshifts can be extended to an n-to-1 code between irreducible shifts of finite type for all large n. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | symbolic dynamics | - |
dc.subject | shift of finite type | - |
dc.subject | sofic shift | - |
dc.subject | entropy | - |
dc.subject | 기호동역학 | - |
dc.subject | 유한형 천이공간 | - |
dc.subject | 그래프형 천이공간 | - |
dc.subject | 엔트로피 | - |
dc.subject | symbolic dynamics | - |
dc.subject | shift of finite type | - |
dc.subject | sofic shift | - |
dc.subject | entropy | - |
dc.subject | 기호동역학 | - |
dc.subject | 유한형 천이공간 | - |
dc.subject | 그래프형 천이공간 | - |
dc.subject | 엔트로피 | - |
dc.title | Topological properties of factor maps in symbolic dynamics | - |
dc.title.alternative | 기호동역학에서 인수함수의 위상적 성질에 관한 연구 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 327747/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020047551 | - |
dc.contributor.localauthor | Shin, Su-Jin | - |
dc.contributor.localauthor | 신수진 | - |
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