東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Dynamics on the Moduli Space of Non-...

Khan, Sayantan.

Linked to FindBook

Google Book

Amazon

博客來

Dynamics on the Moduli Space of Non-Orientable Surfaces.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamics on the Moduli Space of Non-Orientable Surfaces./
Author:	Khan, Sayantan.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
Description:	126 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31348953
ISBN:	9798382739304

Dynamics on the Moduli Space of Non-Orientable Surfaces.
Khan, Sayantan.

Dynamics on the Moduli Space of Non-Orientable Surfaces. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 126 p.

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--University of Michigan, 2024.

The moduli spaces of non-orientable hyperbolic surfaces have conjectural similarities to infinite volume geometrically finite hyperbolic manifolds. This thesis establishes some of the conjectured analogies to geometrically finite hyperbolic manifolds, which are useful in the context of understanding the geodesic flow on the unit cotangent bundle of the moduli space. In particular, it is shown that the Patterson-Sullivan measure is supported on the set of projective measured foliations containing no one-sided leaves. We then also show that the action of the mapping class group on the Teichmuller space, restricted to a finite covolume subset, is statistically convex-cocompact. We deduce from this that the Patterson-Sullivan measure is non-atomic, and the Bowen-Margulis measure on the unit cotangent bundle is finite, and the geodesic flow is ergodic with respect to this measure.

ISBN: 9798382739304Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Geometry

Dynamics on the Moduli Space of Non-Orientable Surfaces.
LDR:02011nmm a2200373 4500 001 2400008
005 20240916070041.5
006 m o d
007 cr#unu||||||||
008 251215s2024 ||||||||||||||||| ||eng d
020 $a 9798382739304
035 $a (MiAaPQ)AAI31348953
035 $a (MiAaPQ)umichrackham005512
035 $a AAI31348953
040 $a MiAaPQ $c MiAaPQ
100 1 $a Khan, Sayantan. $3 3769981
245 1 0 $a Dynamics on the Moduli Space of Non-Orientable Surfaces.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 126 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisor: Wright, Alexander;Spatzier, Ralf.
502 $a Thesis (Ph.D.)--University of Michigan, 2024.
520 $a The moduli spaces of non-orientable hyperbolic surfaces have conjectural similarities to infinite volume geometrically finite hyperbolic manifolds. This thesis establishes some of the conjectured analogies to geometrically finite hyperbolic manifolds, which are useful in the context of understanding the geodesic flow on the unit cotangent bundle of the moduli space. In particular, it is shown that the Patterson-Sullivan measure is supported on the set of projective measured foliations containing no one-sided leaves. We then also show that the action of the mapping class group on the Teichmuller space, restricted to a finite covolume subset, is statistically convex-cocompact. We deduce from this that the Patterson-Sullivan measure is non-atomic, and the Bowen-Margulis measure on the unit cotangent bundle is finite, and the geodesic flow is ergodic with respect to this measure.
590 $a School code: 0127.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Geometry
653 $a Topology
653 $a Dynamics
653 $a Finite hyperbolic manifold
690 $a 0405
690 $a 0642
710 2 $a University of Michigan. $b Mathematics. $3 3185260
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0127
791 $a Ph.D.
792 $a 2024
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31348953