Displaying similar documents to “Invariant Measures and Orbit Closures for Unipotent Action on Homogeneous Spaces (Survey).”

Minimality and unique ergodicity for subgroup actions

Shahar Mozes, Barak Weiss (1998)

Annales de l'institut Fourier

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Let G be an -algebraic semisimple group, H an algebraic -subgroup, and Γ a lattice in G . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of H on G / Γ is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on G / Γ invariant under unipotent elements, and the study of “tubes” in G / Γ .

Fixed point theory for homogeneous spaces, II

Peter Wong (2005)

Fundamenta Mathematicae

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Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously...