Search

3 results

Most of the Maps near the Exponential are Hyperbolic
Xiumei Wang, Gaofei Zhang
Journal:

Nagoya Mathematical Journal / Volume 191 / 2008

Published online by Cambridge University Press:

11 January 2016, pp. 135-148

Print publication:

2008
- Article
- - You have access
- PDF
- Export citation
Let fλ(z) = λez. In this short note, we consider those maps fλ with λ close to 1. We show that the probability that fλ is hyperbolic approaches 1 as λ → 1.

Iteration of Analytic Multifunctions
Maciej Klimek
Journal:

Nagoya Mathematical Journal / Volume 162 / June 2001

Published online by Cambridge University Press:

22 January 2016, pp. 19-40

Print publication:

June 2001
- Article
- - You have access
- PDF
- Export citation
It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in CN. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in CN, depend analytically on the generating polynomials, in the sense of the theory of analytic set-valued functions. It is also proved that every pluriregular set can be approximated by composite Julia sets. Finally, iteration of infinitely many polynomial mappings is used to give examples of pluriregular sets which are not composite Julia sets and on which Markov’s inequality fails.

Non-Real Periodic Points of Entire Functions
Walter Bergweiler
Journal:

Canadian Mathematical Bulletin / Volume 40 / Issue 3 / 01 September 1997

Published online by Cambridge University Press:

20 November 2018, pp. 271-275

Print publication:

01 September 1997
- Article
- - You have access
- PDF
- Export citation
It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.