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Dynamics on Hubbard trees

100%

Alsedà L., Fagella N.

Fundamenta Mathematicae

2000

tom 164

nr 2

115-141

It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type. Moreover, we study dynamical features such as entropy, transitivity or periodic structure of the polynomial restricted to the Hubbard tree, and compare them with the properties of the polynomial on its Julia set. In other words, we want to study how much of the "dynamical information" about the polynomial is captured by the Hubbard tree.

On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points II

81%

Fagella N., Jarque X., Taixés J.

Fundamenta Mathematicae

2011

tom 215

nr 2

177-202

Following the attracting and preperiodic cases, in this paper we prove the existence of weakly repelling fixed points for transcendental meromorphic maps, provided that their Fatou set contains a multiply connected parabolic basin. We use quasi-conformal surgery and virtually repelling fixed point techniques.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Fagella N.

1 Alsedà L.

1 Jarque X.

1 Taixés J.

1 2011

1 2000

Wyniki wyszukiwania

Dynamics on Hubbard trees

On connectivity of Julia sets of transcendental meromorphic maps and weakly repelling fixed points II