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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 23656, 20 pages
http://dx.doi.org/10.1155/IJMMS/2006/23656

Horoballs in simplices and Minkowski spaces

1Department of Mathematics, Royal Institute of Technology, Stockholm 10044, Sweden
2Faculty of Mathematics, Bielefeld University, Bielefeld 33501, Germany
3Sobolev Institute of Mathematics, Pevtsova 13, Omsk 644099, Russia

Received 5 August 2005; Revised 23 July 2006; Accepted 25 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.