Criterion for rays landing together
نویسندگان
چکیده
منابع مشابه
A Landing Theorem for Periodic Rays of Exponential Maps
For the family of exponential maps z 7→ exp(z) + κ, we show the following analog of a theorem of Douady and Hubbard concerning polynomials. Suppose that g is a periodic external ray of an exponential map with nonescaping singular value. Then g lands at a repelling or parabolic periodic point. We also show that there are periodic external rays landing at all periodic points of such an exponentia...
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The landing property of the stretching rays in the parameter space of bimodal real cubic polynomials is completely determined. Define the Böttcher vector by the difference of escaping two critical points in the logarithmic Böttcher coordinate. It is a stretching invariant in the real shift locus. We show that stretching rays with non-integral Böttcher vectors have non-trivial accumulation sets ...
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A transcendental entire function f is called geometrically finite if the intersection of the set S(f) of singular values with the Fatou set F(f) is compact and the intersection of the postsingular set P (f) with the Julia set J (f) is finite. (In particular, this includes all entire functions with finite postsingular set.) If f is geometrically finite, then F(f) is either empty or consists of t...
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We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2020
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/8088