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

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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.
Shin, Su-Jinresearcher신수진researcher
한국과학기술원 : 수리과학과,
Issue Date
327747/325007  / 020047551

학위논문(박사) - 한국과학기술원 : 수리과학과, 2009. 8., [ iii, 82 p. ]


symbolic dynamics; shift of finite type; sofic shift; entropy; 기호동역학; 유한형 천이공간; 그래프형 천이공간; 엔트로피; symbolic dynamics; shift of finite type; sofic shift; entropy; 기호동역학; 유한형 천이공간; 그래프형 천이공간; 엔트로피

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