Treffer: A Tits alternative for endomorphisms of the projective line.

We prove an analog of the Tits alternative for endomorphisms of P1. In particular, we show that if S is a finitely generated semigroup of endomorphisms of P1 over C, then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field of any characteristic and Prep.f / 6D Prep.g/, then for all sufficiently large j, the semigroup hf j; gj i is a free semigroup on two generators. [ABSTRACT FROM AUTHOR]

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