math.DS — Dynamical Systems

Stable Algebraic Families for $\mathbb{P}^2$

Contributed by Jit Wu Yap

We classify one-dimensional families of endomorphisms on $\mathbb{P}^2$ that are algebraically stable, generalizing a theorem of McMullen. The non-isotrivial families are either homogeneous lifts of flexible Lattes maps on $\mathbb{P}^1$, or a family of Lattes maps arising from abelian surfaces.