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Growth Indicators and Conformal Measures for Transverse Groups and Ergodic Dichotomy for Subspace Flows in Higher Rank
Growth Indicators and Conformal Measures for Transverse Groups and Ergodic Dichotomy for Subspace Flows in Higher Rank
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103027
- ISBN
- 9798286441648
- DDC
- 510
- 저자명
- Wang, Yahui.
- 서명/저자
- Growth Indicators and Conformal Measures for Transverse Groups and Ergodic Dichotomy for Subspace Flows in Higher Rank
- 발행사항
- [Sl] : Yale University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 166 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: A.
- 주기사항
- Advisor: Oh, Hee.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2025.
- 초록/해제
- 요약Let G be a connected semisimple real algebraic group. The class of transverse subgroups of G includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov or relatively Anosov subgroups. Given a transverse subgroup Gamma, we show that the Gamma-action on the Weyl chamber flow space determined by its limit set is properly discontinuous. This allows us to consider the quotient space and define Bowen-Margulis-Sullivan measures.We then study the ergodicity of a one-parameter diagonalizable subgroup of G acting on the aforementioned quotient space, equipped with a Bowen-Margulis-Sullivan measure. We obtain an ergodicity criterion similar to the Hopf-Tsuji-Sullivan dichotomy for the ergodicity of the geodesic flow on hyperbolic manifolds. In addition, we extend this criterion to the action of any connected diagonal subgroup of arbitrary dimension. This provides a codimension dichotomy on the ergodicity of a connected diagonalizable subgroup for general Anosov subgroups, generalizing an earlier work by Burger-Landesberg-Lee-Oh for Borel Anosov subgroups.We also introduce the notion of growth indicators and discuss their properties and roles in the study of conformal measures, extending the work of Quint. Moreover, we explore its applications to general Anosov subgroups and obtain some correspondence on conformal measures similar to an earlier work by Lee-Oh for Borel Anosov subgroups.
- 일반주제명
- Mathematics
- 일반주제명
- Mathematics education
- 키워드
- Anosov subgroups
- 키워드
- Quotient space
- 기타저자
- Yale University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103027
■006m o d
■007cr#unu||||||||
■020 ▼a9798286441648
■035 ▼a(MiAaPQ)AAI31845374
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aWang, Yahui.
■24510▼aGrowth Indicators and Conformal Measures for Transverse Groups and Ergodic Dichotomy for Subspace Flows in Higher Rank
■260 ▼a[Sl]▼bYale University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a166 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: A.
■500 ▼aAdvisor: Oh, Hee.
■5021 ▼aThesis (Ph.D.)--Yale University, 2025.
■520 ▼aLet G be a connected semisimple real algebraic group. The class of transverse subgroups of G includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov or relatively Anosov subgroups. Given a transverse subgroup Gamma, we show that the Gamma-action on the Weyl chamber flow space determined by its limit set is properly discontinuous. This allows us to consider the quotient space and define Bowen-Margulis-Sullivan measures.We then study the ergodicity of a one-parameter diagonalizable subgroup of G acting on the aforementioned quotient space, equipped with a Bowen-Margulis-Sullivan measure. We obtain an ergodicity criterion similar to the Hopf-Tsuji-Sullivan dichotomy for the ergodicity of the geodesic flow on hyperbolic manifolds. In addition, we extend this criterion to the action of any connected diagonal subgroup of arbitrary dimension. This provides a codimension dichotomy on the ergodicity of a connected diagonalizable subgroup for general Anosov subgroups, generalizing an earlier work by Burger-Landesberg-Lee-Oh for Borel Anosov subgroups.We also introduce the notion of growth indicators and discuss their properties and roles in the study of conformal measures, extending the work of Quint. Moreover, we explore its applications to general Anosov subgroups and obtain some correspondence on conformal measures similar to an earlier work by Lee-Oh for Borel Anosov subgroups.
■590 ▼aSchool code: 0265.
■650 4▼aMathematics
■650 4▼aMathematics education
■653 ▼aAnosov subgroups
■653 ▼aHopf-Tsuji-Sullivan dichotomy
■653 ▼aQuotient space
■690 ▼a0405
■690 ▼a0280
■71020▼aYale University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12A.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356740▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
