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HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES
Author Info
Yang, Lei
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1401466357
Abstract Details
Year and Degree
2014, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In my thesis, I will study the product space of unit tangent bundles of several non-compact hyperbolic spaces, and consider the diagonal geodesic flow on this product space. We define the divergent set to be the collection of points whose forward trajectories under the diagonal geodesic flow diverge. The aim of this thesis is to calculate the Hausdorff dimension of the divergent set. If we assume every component has finite volume, then the exact value of the Hausdorff dimension is established. If we drop the finite volume condition, but assume every component is geometrically finite, then the lower bound of the Hausdorff dimension is established unconditionally, and if we further assume that every component has the same critical exponent, then it is proved that the given lower bound is the exact value of the Hausdorff dimension.
Committee
Nimish Shah (Advisor)
Jean-Francois Lafont (Committee Member)
Vitaly Bergelson (Committee Member)
Pages
78 p.
Subject Headings
Mathematics
Keywords
hyperbolic spaces
;
geodesic flow
;
Hausdorff dimension
;
Busemann cocycle
;
mixing
;
geometrically finite
;
critical exponent
;
Bowen-Margulis-Sullivan measure
;
Patterson-Sullivan measure
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Citations
Yang, L. (2014).
HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1401466357
APA Style (7th edition)
Yang, Lei.
HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES.
2014. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1401466357.
MLA Style (8th edition)
Yang, Lei. "HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1401466357
Chicago Manual of Style (17th edition)
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Document number:
osu1401466357
Download Count:
720
Copyright Info
© 2014, some rights reserved.
HAUSDORFF DIMENSION OF DIVERGENT GEODESICS ON PRODUCT OF HYPERBOLIC SPACES by Lei Yang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.