DYNAMIC RAYS OF BOUNDED-TYPE TRANSCENDENTAL SELF-MAPS OF THE PUNCTURED PLANE

作者：Fagella Nuria; Marti Pete David^*

来源：Discrete and Continuous Dynamical Systems, 2017, 37(6): 3123-3160.

DOI：10.3934/dcds.2017134

• phrases. Complex dynamics
• transcendental functions
• punctured plane
• escaping set
• dynamic rays
• bounded-type functions

We study the escaping set of functions in the class B-*, that is, transcendental self-maps of C-* for which the set of singular values is contained in a compact annulus of C* that separates zero from infinity. For functions in the class B-*, escaping points lie in their Julia set. If f is a composition of finite order transcendental self-maps of C* (and hence, in the class B-*), then we show that every escaping point of f can be connected to one of the essential singularities by a curve of points that escape uniformly. Moreover, for every sequence e is an element of {0, infinity}(N0), we show that the escaping set of f contains a Cantor bouquet of curves that accumulate to the set {0, infinity} according to e under iteration by f.

• 出版日期2017-6