Spatzier, Ralf Jürgen (1983) Dynamical properties of algebraic systems : a study in closed geodesics. PhD thesis, University of Warwick.

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Abstract

To a great extent, rigidity theory is the study of boundaries of semisimple groups. Here we investigate the action of a lattice on such a boundary. While we can construct topological factors for real rank 1 groups we show the nonexistence of such factors in higher rank for some cases.

We also study the geodesic flow on a compact locally symmetric manifold of the noncompact type. He calculate metric and topological entropies and see that the Liouville measure is a measure or maximal entropy. This leads to a study of compact maximal flats. We give a new proof of their density in the space of all flats. We prove specification and expansiveness theorems for the geodesic flow and apply them to determine a growth rate for compact maximal flats. Finally, we give an example of a space with infinitely many closed singular geodesics.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Geodesics (Mathematics), Rigidity (Geometry)
Official Date:	1983
Dates:	Date Event 1983 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Series, Caroline ; Katok, A. B.
Extent:	[11], 123 leaves
Language:	eng

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