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## О случайном выборе эллиптических и гиперболических поворотов лоренцевых пространств

Чуркин В. А., Ильин А. И.

Elliptic and hyperbolic rotations of the $(n+1)$-dimensional
Lorentz space can be represented as exponential of rank 2 matrices of the
real Lie algebra $so(1, n)$. We shown that the ratio of the volumes of the
corresponding sets of matrices Euclidean norm $<=r$ is equal to $\sqrt{2}^{n-1}-1$
for all $r > 0$. Consequently the portion of hyperbolic rotations near
identity decreases exponentially with increasing n. Another corollary is
that in case of Minkovski space of special relativity choose of elliptic and
hyperbolic rotations near identity is equiprobable.