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Języki publikacji
Abstrakty
The topology and combinatorial structure of the Mandelbrot set $ℳ ^{d}$ (of degree d ≥ 2) can be studied using symbolic dynamics. Each parameter is mapped to a kneading sequence, or equivalently, an internal address; but not every such sequence is realized by a parameter in $ℳ ^{d}$. Thus the abstract Mandelbrot set is a subspace of a larger, partially ordered symbol space, $Λ^{d}$. In this paper we find an algorithm to construct "visible trees" from symbolic sequences which works whether or not the sequence is realized. We use this procedure to find a large class of addresses that are nonrealizable, and to prove that all such trees in $Λ^{d}$ actually satisfy the Translation Principle (in contrast to $ℳ ^{d}$). We also study how the existence of a hyperbolic component with a given address depends on the degree d: addresses can be sorted into families so that at least one address of each family is realized for sufficiently large d.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
35-87
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Department of Mathematics, P.O. Box 35, FIN-40014 University of Jyväskylä, Finland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-4