Geodesic
On Asymptotic Behavior and Rectangular Band Structures in SL(2, R)
Journal of Lie Theory, Tome 11 (2001) no. 2, pp. 559-604

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We associate with every subsemigroup of Sl(2, R), not contained in a single Borel group, an "asymptotic object", a rectangular band which is defined on a closed subset of a torus surface. Using this concept we show that the horizon set (in the sense of J. D. Lawson [J. Lie Theory 4 (1994) 17--29]) of a connected open subsemigroup of Sl(2, R) is always convex, in fact the interior of a three dimensional Lie semialgebra. Other applications include the classification of all exponential subsemigroups of Sl(2, R) and the asymptotics of semigroups of integer matrices in Sl(2, R).
Classification : 22E15, 22E67, 22E46, 22A15, 22A25
Mots-clés : Asymptotic objects, asymptotic property, subsemigroups of Sl(2, R), Lie semigroups, Lie semialgebras and their classification, compression semigroups, diamond product, rectangular domain, umbrella sets, control theory in Lie groups, asymptotics of integer 
B. E. Breckner; W. A. F. Ruppert. On Asymptotic Behavior and Rectangular Band Structures in SL(2, R). Journal of Lie Theory, Tome 11 (2001) no. 2, pp. 559-604. http://geodesic.mathdoc.fr/item/JOLT_2001_11_2_a15/
@article{JOLT_2001_11_2_a15,
     author = {B. E. Breckner and W. A. F. Ruppert},
     title = {On {Asymptotic} {Behavior} and {Rectangular} {Band} {Structures} in {SL(2,} {R)}},
     journal = {Journal of Lie Theory},
     pages = {559--604},
     year = {2001},
     volume = {11},
     number = {2},
     zbl = {0982.22005},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_2_a15/}
}
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