Topological properties of factor maps in symbolic dynamics기호동역학에서 인수함수의 위상적 성질에 관한 연구

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dc.contributor.advisorShin, Su-Jin-
dc.contributor.advisor신수진-
dc.contributor.authorJung, Ui-Jin-
dc.contributor.author정의진-
dc.date.accessioned2011-12-14T04:40:39Z-
dc.date.available2011-12-14T04:40:39Z-
dc.date.issued2009-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=327747&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41927-
dc.description학위논문(박사) - 한국과학기술원 : 수리과학과, 2009. 8., [ iii, 82 p. ]-
dc.description.abstractWe 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.languageeng-
dc.publisher한국과학기술원-
dc.subjectsymbolic dynamics-
dc.subjectshift of finite type-
dc.subjectsofic shift-
dc.subjectentropy-
dc.subject기호동역학-
dc.subject유한형 천이공간-
dc.subject그래프형 천이공간-
dc.subject엔트로피-
dc.subjectsymbolic dynamics-
dc.subjectshift of finite type-
dc.subjectsofic shift-
dc.subjectentropy-
dc.subject기호동역학-
dc.subject유한형 천이공간-
dc.subject그래프형 천이공간-
dc.subject엔트로피-
dc.titleTopological properties of factor maps in symbolic dynamics-
dc.title.alternative기호동역학에서 인수함수의 위상적 성질에 관한 연구-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN327747/325007 -
dc.description.department한국과학기술원 : 수리과학과, -
dc.identifier.uid020047551-
dc.contributor.localauthorShin, Su-Jin-
dc.contributor.localauthor신수진-
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MA-Theses_Ph.D.(박사논문)
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