- Tytuł:
- Jordan tori and polynomial endomorphisms in $ℂ^2$
- Autorzy:
-
Denker, Manfred
Heinemann, Stefan - Powiązania:
- https://bibliotekanauki.pl/articles/1205309.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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).
- Źródło:
-
Fundamenta Mathematicae; 1998, 157, 2-3; 139-159
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł