Orbits of euclidean frames under discrete linear groups

Dani, S. G.; Raghavan, S.

doi:10.1007/bf02762053

Cited by 39 publications

(31 citation statements)

References 8 publications

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“…We observe that it follows from general results of Dani and Raghavan on linear actions [9] that the orbits of Γ = SL(d, Z) acting on T d are finite or dense. In this direction a detailed study of Γ-orbits in R d of a general subgroup Γ ⊂ SL(d, R) was developed by Conze and Guivarc'h in [7].…”

Section: Introduction and Main Resultsmentioning

confidence: 58%

Semigroup actions on tori and stationary measures on projective spaces

Guivarc’h

Urban

2005

Studia Math.

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Abstract. Let Γ be a sub-semigroup of G = GL(d, R), d > 1. We assume that the action of Γ on R d is strongly irreducible and that Γ contains a proximal and expanding element. We describe contraction properties of the dynamics of Γ on R d at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space P d−1 . In the case where Γ is a sub-semigroup of GL(d, R)∩M (d, Z) and Γ has the above properties, we deduce that the Γ-orbits on

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Section: Introduction and Main Resultsmentioning

confidence: 58%

Semigroup actions on tori and stationary measures on projective spaces

Guivarc’h

Urban

2005

Studia Math.

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“…This is proved in [4] by a different method. A similar result is expected to be true in greater generality.…”

Section: Let Nbea Maximal Horospherical Subgroup Of G Let a Be An N-mentioning

confidence: 91%

Dynamics of horospherical flows

Dani¹

1980

Bull. Amer. Math. Soc.

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“…The second assertion in the theorem follows from the proof of Proposition 4.3 in [11]; in the statement of the proposition there, the conclusion as above is claimed under a weaker hypothesis, which however is incorrect.…”

Section: Duality and Values Of Linear Formsmentioning

confidence: 93%

“…[11]). Consider the action of SL(n, Z Z) on E p given by the componentwise action on each copy of IR n .…”

Section: Duality and Values Of Linear Formsmentioning

confidence: 99%