Autor: Barański, Krzysztof - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: From Newton’s method to exotic basins Part I: The parameter space
Autorzy:: Barański, Krzysztof
Powiązania:: https://bibliotekanauki.pl/articles/1205287.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: This is the first part of the work studying the family $\mathfrak{F}$ of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of $\mathfrak{F}$ and give a detailed study of the subfamily $ℱ_2$ consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in $ℱ_2$ from Newton maps to maps with so-called exotic basins.
Źródło:: Fundamenta Mathematicae; 1998, 158, 3; 249-288
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Hausdorff dimension and measures on Julia sets of some meromorphic maps
Autorzy:: Barański, Krzysztof
Powiązania:: https://bibliotekanauki.pl/articles/1208335.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: We study the Julia sets for some periodic meromorphic maps, namely the maps of the form $f(z) = h(exp \frac{2πi}{T}z)$ where h is a rational function or, equivalently, the maps $˜f(z) = exp (\frac{2πi}{h}(z))$. When the closure of the forward orbits of all critical and asymptotic values is disjoint from the Julia set, then it is hyperbolic and it is possible to construct the Gibbs states on J(˜f) for -α log |˜˜f|. For ˜α = HD(J(˜f)) this state is equivalent to the ˜α-Hausdorff measure or to the ˜α-packing measure provided ˜α is greater or smaller than 1. From this we obtain some lower bound for HD(J(f)) and real-analyticity of HD(J(f)) with respect to f. As an example the family $f_λ(z)=λ tan z$ is studied. We estimate $HD(J(f_λ))$ near λ = 0 and show it is a monotone function of real λ.
Źródło:: Fundamenta Mathematicae; 1995, 147, 3; 239-260
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

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