Wandering domains for composition of entire functions
نویسندگان
چکیده
منابع مشابه
Wandering Domains in the Iteration of Compositions of Entire Functions
If p is entire, g(z) = a+ b exp(2πi/c) , where a , b , c are non-zero constants and the normal set of g(p) has no wandering components, then the same is true for the normal set of p(g) . Let f be a rational function of degree at least 2 or a nonlinear entire function. Let f , for n ∈ N denote the nth iterate of f . Denote the set of normality by N(f) and the Julia set by J(f) . Thus N(f) = {z :...
متن کاملWandering Domains in the Iteration of Entire Functions
N(f) is the 'set of normality' and J(f) is the 'Fatou-Julia' set for / . By definition, N(f) is open (possibly empty). It is easily shown (see, for example, [6,7]) that J(f) is non-empty and perfect, and, further, that J{f) is completely invariant under mapping by / , by which is meant that z e J(f) implies both /(z) e J(f) and c e J(f) for any c which satisfies f(c) = z. Also N(f) is completel...
متن کاملWandering Domains in the Iteration Ofcompositions of Entire Functionsi
If p is entire, g(z) = a + b exp(2i=c), where a , b , c are non-zero constants and the normal set of g(p) has no wandering components, then the same is true for the normal set of p(g). Let f be a rational function of degree at least 2 or a nonlinear entire function. Let f n , for n 2 N denote the nth iterate of f. Denote the set of normality by N(f) and the Julia set by J(f). Thus N(f) = fz : (...
متن کاملAn Entire Function with Simply and Multiply Connected Wandering Domains
We modify a construction of Kisaka and Shishikura to show that there exists an entire function f which has both a simply connected and a multiply connected wandering domain. Moreover, these domains are contained in the set A(f) consisting of the points where the iterates of f tend to infinity fast. The results answer questions by Rippon and Stallard.
متن کاملDeformation of Entire Functions with Baker Domains
We consider entire transcendental functions f with an invariant (or periodic) Baker domain U. First, we classify these domains into three types (hyperbolic, simply parabolic and doubly parabolic) according to the surface they induce when we quotient by the dynamics. Second, we study the space of quasiconformal deformations of an entire map with such a Baker domain by studying its Teichmüller sp...
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: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.04.020