For a class of superattracting germs in C^2, the super-stable set W is a uniformly laminar Cantor bouquet of analytic curves, represented by integrating over curves parameterized by a non-Archimedean invariant measure.
On the dynamical Manin-Mumford conjecture for plane polynomial maps
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abstract
We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteristic 0.
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Polynomial skew products with small relative degree
For a class of superattracting germs in C^2, the super-stable set W is a uniformly laminar Cantor bouquet of analytic curves, represented by integrating over curves parameterized by a non-Archimedean invariant measure.