Dynamics of braids땋임 동역학

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In this thesis we study the dynamics of braids using the folding decomposition of train track maps and the entropy. In Chapter 1 we explain the preliminaries about braids, the Nielsen-Thurston classification of surface homeomorphisms, and the train track algorithm. In Chapter 2 we show that the entropy of a braid can be computed from the spectral radius of the Burau matrix of another braid after reviewing the topological entropy of braid and the Burau representation. In Chapter 3 we introduce the folding decomposition of train track maps and show that for each braid index there are finitely many folding automata which generate all the conjugacy classes of pseudo-Anosov braids. In Chapter 4 we use the folding automata to find the braid with the minimal non-trivial entropy for braid index less than 6. In Chapter 5 we estimate the minimal entropy of braids with general braid index and show that the entropy of a pseudo-Anosov pure braid is greater than or equal to $\log 3$.
Advisors
Ko, Ki-Hyoungresearcher고기형researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2002
Identifier
177221/325007 / 000985185
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2002.8, [ [ii], 68 p. ]

Keywords

entropy; braid; topological dynamics; 위상동역학; 엔트로피; 땋임

URI
http://hdl.handle.net/10203/41852
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=177221&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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