Title: Short proofs of theorems of Malyutin and Margulis
Abstract: The Ghys-Margulis alternative asserts that a subgroup $G$ of homeomorphisms of the circle which does not contain a free subgroup on two generators must admit an invariant probability measure. Malyutinâs theorem classifies minimal actions of $G$. We present a short proof of Malyutinâs theorem and then deduce Margulisâ theorem which confirms the G-M alternative. The basic ideas are borrowed from the original work of Malyutin, but our proof is considerably shorter.