Jordan tori and polynomial endomorphisms in $ℂ^2$
Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 139-159
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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).
@article{10_4064_fm_157_2_3_139_159,
author = {Manfred Denker and Stefan-M. Heinemann},
title = {Jordan tori and polynomial endomorphisms in $\ensuremath{\mathbb{C}}^2$},
journal = {Fundamenta Mathematicae},
pages = {139--159},
year = {1998},
volume = {157},
number = {2},
doi = {10.4064/fm-157-2-3-139-159},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-139-159/}
}
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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
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