Decompositions of factor codes = 인수함수의 분할에 관한 연구

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The purpose of this work is to present the properties of sliding block codes between shift spaces, especially the existence, the extension and the decomposition. We investigate the existence and the extension of graph homomorphisms. We prove that for given two graphs there is a bi-resolving (or bi-covering) graph homomorphism between them exactly when their adjacency matrices satisfy certain matrix relations in Chapter 3. We give some sufficient conditions for a bi-resolving graph homomorphism to have a bi-covering extension with an irreducible domain, and prove that any bi-closing code between shift spaces can be extended to an $\It{n}$-to-1 code between irreducible shifts of finite type for all large $\It{n}$. In Chapter 4 we prove that for any embedding from a shift space to a mixing shift of finite type and for any number $\It{h}$ lying between their entropies, there exists a decomposition of the given code such that the intermediate shift space has $\It{h}$ as its entropy. We show that this does not hold when an embedding is replaced with a factor code. We present some conditions for a factor code between shift spaces to have a decomposition.
Advisors
Shin, Su-Jinresearcher신수진researcher
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
455385/325007  / 020037491
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.08, [ ii, 54 p. ]

Keywords

shift space; 엔트로피; 인수함수; 천이공간; 기호동역학; entropy; factor code; symbolic dynamics

URI
http://hdl.handle.net/10203/41946
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=455385&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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