Geodesic
Jordan tori and polynomial endomorphisms in $ℂ^2$
Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 139-159.

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For a class of quadratic polynomial endomorphisms $f: ℂ^2 → ℂ^2$ close to the standard torus map $(x,y) → (x^2,y^2)$, we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).
DOI : 10.4064/fm-157-2-3-139-159

Manfred Denker 1 ; Stefan-M. Heinemann 1

1 
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Manfred Denker; Stefan-M. Heinemann. Jordan tori and polynomial endomorphisms in $ℂ^2$. Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 139-159. doi : 10.4064/fm-157-2-3-139-159. http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-139-159/

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