Geodesic
Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups
Journal of Lie theory, Tome 24 (2014) no. 1, pp. 259-305.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $G$ be a real semisimple Lie group with trivial centre and no compact factors. Given a conjugate pair of either real hyperbolic elements or unipotent elements $a$ and $b$ in $G$ we find a conjugating element $g \in G$ such that $d_G(1,g) \leq L(d_G(1,u)+d_G(1,v))$, where $L$ is a positive constant which will depend on some property of $a$ and $b$ (when $a,b$ are unipotent we require that the Lie algebra of $G$ is split). For the vast majority of such elements however, $L$ can be assumed to be a uniform constant.
Classification : 20F65, 20F10, 22E46, 53C35
Mots-clés : Geometric group theory, conjugacy problem, semisimple Lie groups 
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     author = {A. Sale },
     title = {Bounded {Conjugators} for {Real} {Hyperbolic} and {Unipotent} {Elements} in {Semisimple} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {259--305},
     publisher = {mathdoc},
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     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_1_JLT_2014_24_1_a11/}
}
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A. Sale . Bounded Conjugators for Real Hyperbolic and Unipotent Elements in Semisimple Lie Groups. Journal of Lie theory, Tome 24 (2014) no. 1, pp. 259-305. http://geodesic.mathdoc.fr/item/JLT_2014_24_1_JLT_2014_24_1_a11/