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Polterovich and Z. Rudnick considered the behavior of a one-parameter subgroup of a Lie group under the influence of a sequence of kicks. Among others they raise the following problem: {\\it is the horocycle flow stably quasi-mixing on $SL(2,\\mathbb{R})/\\Gamma$?} Equivalently it can be reformulated in terms of boundedness of the sequences of products $\nP_n(t) = \\Phi_n H(t)\\Phi_{n-1} H(t) \\, ... \\, \\Phi_1 H(t) $\nwhere $H(t) = \\begin{pmatrix} 1 & t \n 0 & 1 \\end{pmatrix}$ and $\\Phi=\\{\\Phi_n\\} \\subset SL(2,\\mathbb{R})$. 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