POLYNOMIAL DYNAMIC AND LATTICE ORBITS IN S-ARITHMETIC HOMOGENEOUS SPACES

Homogeneous Twistor Spaces And Nilpotent Orbits

Nondense Orbits of Flows on Homogeneous Spaces

Let F be a nonquasiunipotent one-parameter (cyclic) subgroup of a unimodular Lie group G, Γ a discrete subgroup of G. We prove that for certain classes of subsets Z of the homogeneous space G/Γ, the set of points in G/Γ with F -orbits staying away from Z has full Hausdorff dimension. From this we derive applications to geodesic flows on manifolds of constant negative curvature.

Euler equations on homogeneous spaces and Virasoro orbits

We show that the following three systems related to various hydrodynamical approximations: the Korteweg–de Vries equation, the Camassa–Holm equation, and the Hunter–Saxton equation, have the same symmetry group and similar bihamiltonian structures. It turns out that their configuration space is the Virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow ...

Divergent Torus Orbits in Homogeneous Spaces of Qrank Two

Let G be a semisimple algebraic Qgroup. let. F be an arithmetic subgroup of G . and let, T be an E-split torus in G . We prove that if there is a divergent Tn-orbit in r \ G R , and Q-rank G < 2, t,hen dim T < Q-rankG. This provides a partial answer to a question of G . Tomanov and B. Weiss.

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...