서지주요정보
Dynamics of braids = 땋임 동역학
서명 / 저자 Dynamics of braids = 땋임 동역학 / Won-Taek Song.
발행사항 [대전 : 한국과학기술원, 2002].
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8013613

소장위치/청구기호

학술문화관(문화관) 보존서고

DMA 02010

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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 $\log 3$.

서지기타정보

서지기타정보
청구기호 {DMA 02010
형태사항 [ii], 68 p. : 삽화 ; 26 cm
언어 영어
일반주기 저자명의 한글표기 : 송원택
지도교수의 영문표기 : Ki-Hyoung Ko
지도교수의 한글표기 : 고기형
학위논문 학위논문(박사) - 한국과학기술원 : 수학전공,
서지주기 Reference : p. 63-67
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