Semi-Hyperbolic Maps Are Rare
نویسندگان
چکیده
منابع مشابه
Rational Misiurewicz Maps Are Rare
Set P 0(f, c) = P (f, c). The set P (f) = P 0(f) is the postcritical set of f . We will also use the notion postcritical set for P k(f) for some suitable k ≥ 0. Denote by J(f) the Julia set of f and F (f) the Fatou set of f . Recall that the ω-limit set ω(x) of a point x is the set of all limit points of ∪n≥0f n(x). A periodic point x with period p is a sink if there is a neighborhood around x ...
متن کاملSemi-hyperbolic fibered rational maps and rational semigroups
This paper is based on the author’s previous work [S4]. We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are uniformly perfect. From this result, we show that, for any semigroup G generated by a com...
متن کاملRational Misiurewicz Maps Are Rare Ii
The notion of Misiurewicz maps has its origin from the paper [10] from 1981 by M. Misiurewicz. The (real) maps studied in this paper have, among other things, no sinks and the omega limit set ω(c) of every critical point c does not contain any critical point. In particular, in the quadratic family fa(x) = 1 − ax 2, where a ∈ (0, 2), a Misiurewicz map is a non-hyperbolic map where the critical p...
متن کاملHyperbolic Semi-adequate Links
We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently complicated positive braids are hyperbolic links.
متن کاملHyperbolic Components of Mcmullen Maps
In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen’s theorem that cusps are dense on the Bers’ boundary of Teichmüller...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2017
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnx056