Horoballs in simplices and Minkowski spaces

Horoballs in simplices and Minkowski spaces

We obtain precise descriptions of all horoballs for Hilbert's geometry on simplices and for normed finite-dimensional vector spaces with norm given by some polyhedron. Certain geometrical consequences are deduced and several other applications are pointed out, which concern the dynamics of impo...

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Main Authors: A. Karlsson, V. Metz, G. A. Noskov
Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS/2006/23656
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spelling doaj-64fa2b9550af4d86ba7648fd559457662020-11-25T00:33:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/2365623656Horoballs in simplices and Minkowski spacesA. Karlsson0V. Metz1G. A. Noskov2Department of Mathematics, Royal Institute of Technology, Stockholm 10044, SwedenFaculty of Mathematics, Bielefeld University, Bielefeld 33501, GermanySobolev Institute of Mathematics, Pevtsova 13, Omsk 644099, RussiaWe obtain precise descriptions of all horoballs for Hilbert's geometry on simplices and for normed finite-dimensional vector spaces with norm given by some polyhedron. Certain geometrical consequences are deduced and several other applications are pointed out, which concern the dynamics of important classes of nonlinear self-maps of convex cones.http://dx.doi.org/10.1155/IJMMS/2006/23656
collection DOAJ
language English
format Article
sources DOAJ
author A. Karlsson
V. Metz
G. A. Noskov
spellingShingle A. Karlsson
V. Metz
G. A. Noskov
Horoballs in simplices and Minkowski spaces
International Journal of Mathematics and Mathematical Sciences
author_facet A. Karlsson
V. Metz
G. A. Noskov
author_sort A. Karlsson
title Horoballs in simplices and Minkowski spaces
title_short Horoballs in simplices and Minkowski spaces
title_full Horoballs in simplices and Minkowski spaces
title_fullStr Horoballs in simplices and Minkowski spaces
title_full_unstemmed Horoballs in simplices and Minkowski spaces
title_sort horoballs in simplices and minkowski spaces
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2006-01-01
description We obtain precise descriptions of all horoballs for Hilbert's geometry on simplices and for normed finite-dimensional vector spaces with norm given by some polyhedron. Certain geometrical consequences are deduced and several other applications are pointed out, which concern the dynamics of important classes of nonlinear self-maps of convex cones.
url http://dx.doi.org/10.1155/IJMMS/2006/23656
work_keys_str_mv AT akarlsson horoballsinsimplicesandminkowskispaces
AT vmetz horoballsinsimplicesandminkowskispaces
AT ganoskov horoballsinsimplicesandminkowskispaces
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