Winning Sets and Hyperbolic Geometry
Exploring the Riemannian metric in hyperbolic spaces
by Neel Kumari*,
- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659
Volume 4, Issue No. 7, Nov 2012, Pages 0 - 0 (0)
Published by: Ignited Minds Journals
ABSTRACT
Let,the hyperbolic space of dimension d+1. For d= 1 it is the upper half plane, known also as the Poincarupper half plane, consisting of complexnumbers with positive imaginary part. Hd+1 is equipped with theRiemannian metric
KEYWORD
winning sets, hyperbolic geometry, hyperbolic space, dimension, Poincaré upper half plane, complex numbers, Riemannian metric
2. M.B. Bekka and M. Mayer, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, London Mathematical Society Lecture Note Series, 269, Cambridge University Press, Cambridge, 2000. 3. J.W.S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, 1957. 4. S.G. Dani, Bounded orbits of flows on homogenous spaces, Comment. Math. Helv. 61 (1986), 636-660. 5. S.G. Dani, On orbits of endomorphisms of tori and the Schmidt game, Ergod. Th. and Dynam. Syst. 8 (1988), 523-529. 6. D. Kleinbock and B. Weiss, Badly approximable vectors on fractals Israel J. Math. 149 (2005), 137-170. 7. W.M. Schmidt, On badly approximable numbers and certain games, Trans. Amer. Math. Soc. 123 (1966), 178-199. 8. W.M. Schmidt, Diophantine Approximation, Springer Verlag 1980. 9. S.G. Dani and G.A. Margulis, Orbit closures of generic unipotent flows on homogeneous spaces of SL(3,IR), Math. Ann. 286 (1990), 101-128. 10. P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer Verlag, 1982.
