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Asymptotic behavior and Denjoy-Wolff theorems for Hilbert metric nonexpansive maps

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TitleInfo (displayLabel = Citation Title); (type = uniform)
Title
Asymptotic behavior and Denjoy-Wolff theorems for Hilbert metric nonexpansive maps
Name (ID = NAME001); (type = personal)
NamePart (type = family)
Lins
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Brian C.
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Brian C. Lins
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author
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Nussbaum
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Roger
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Roger D Nussbaum
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Luo
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Feng
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Advisory Committee
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Feng Luo
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internal member
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Huang
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Xiaojun
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Advisory Committee
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Xiaojun Huang
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Karlsson
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Anders
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Advisory Committee
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Anders Karlsson
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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Text
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theses
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DateCreated (qualifier = exact)
2007
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2007
Language
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English
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electronic
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v, 86 pages
Abstract
We study the asymptotic behavior of fixed point free Hilbert metric nonexpansive maps on bounded convex domains. For such maps, we prove that the omega limit sets are contained in a convex subset of the boundary when the domain is either polyhedral or two dimensional. Similar results are obtained for several classes of positive operators defined on closed cones, including linear maps, affine linear maps, max-min operators, and reproduction-decimation operators. We discuss the relationship between these results and other Denjoy-Wolff type theorems. In particular, we investigate the interaction of nonexpansive maps with the horofunction boundary in the Hilbert geometry and in finite dimensional normed spaces.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 82-85).
Subject (ID = SUBJ1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SUBJ2); (authority = ETD-LCSH)
Topic
Metric spaces
Subject (ID = SUBJ3); (authority = ETD-LCSH)
Topic
Mappings (Mathematics)
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16723
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ETD_302
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3XS5VTD
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
Copyright
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Open
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Name
Brian Lins
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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