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We prove that, if $f \\circ \\phi_t=\\varphi_t \\circ f$ for all $t\\geq 0$, then $f$ extends to a homeomorphism of $\\bar{\\mathbb D}$ outside exceptional maximal contact arcs (in particular, for elliptic semigroups, $f$ extends to a homeomorphism of $\\bar{\\mathbb D}$). 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