Article Dans Une Revue American Journal of Mathematics Année : 2022

Rational maps with a preperiodic critical point

Résumé

We show that the set of conjugacy classes of cubic polynomials with a prefixed critical point, of preperiod $k\geq 1$, is an irreducible algebraic curve. We also establish an analogous result for quadratic rational maps. We then study a closely related question concerning the irreducibility (over $\mathbb Q$) of the set of conjugacy classes of unicritical polynomials, of degree $D\geq 2$, with a preperiodic critical point. Our proofs are purely algebraic.

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hal-01970325 , version 1 (23-12-2024)

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Xavier Buff, Adam Epstein, Sarah Koch. Rational maps with a preperiodic critical point. American Journal of Mathematics, 2022, 144 (6), pp.1485-1509. ⟨10.1353/ajm.2022.0036⟩. ⟨hal-01970325⟩
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