The closure of sets of complex exponential functions

1934 ◽  
pp. 86-99
Keyword(s):  
Exponential Functions ◽  
Complex Exponential

Approximation of Lightning Current Waveforms Using Complex Exponential Functions

2016 ◽  
Vol 58 (5) ◽  
pp. 1686-1689 ◽  
Author(s):  
Mirko Yanque Tomasevich ◽  
Antonio C. S. Lima ◽  
Robson F. S. Dias
Keyword(s):  
Exponential Functions ◽  
Lightning Current ◽  
Complex Exponential

COMPARING AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS

2014 ◽  
Vol 15 (1) ◽  
pp. 71-84 ◽  
Author(s):  
P. D’Aquino ◽  
A. Macintyre ◽  
G. Terzo
Keyword(s):  
Analytic Function ◽  
Function Theory ◽  
Research Programme ◽  
Exponential Functions ◽  
Exponential Polynomials ◽  
Zero Sets ◽  
Diophantine Geometry ◽  
Complex Exponential ◽  
Identity Theorem

We continue the research programme of comparing the complex exponential with Zilberś exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for $\mathbb{C}$ using analytic function theory, for example, the Identity Theorem.

Tying hairs for structurally stable exponentials

2000 ◽  
Vol 20 (6) ◽  
pp. 1603-1617 ◽  
Author(s):  
RANJIT BHATTACHARJEE ◽  
ROBERT L. DEVANEY
Keyword(s):  
Fixed Point ◽  
Julia Set ◽  
Basins Of Attraction ◽  
Crucial Importance ◽  
Exponential Functions ◽  
Complex Exponential ◽  
Structurally Stable

Our goal in this paper is to describe the structure of the Julia set of complex exponential functions that possess an attracting cycle. When the cycle is a fixed point, it is known that the Julia set is a ‘Cantor bouquet’, a union of uncountably many distinct curves or ‘hairs’. When the period of the cycle is greater than one, infinitely many of the hairs in the bouquet become pinched or attached together. In this paper, we develop an algorithm to determine which of these hairs are attached. Of crucial importance in this construction is the kneading invariant, a sequence that is derived from the topology of the basins of attraction of the attracting cycle.

scholarly journals A characterization of postcritically minimal Newton maps of complex exponential functions

2018 ◽  
Vol 39 (10) ◽  
pp. 2855-2880
Author(s):  
KHUDOYOR MAMAYUSUPOV
Keyword(s):  
Exponential Function ◽  
Julia Sets ◽  
Exponential Functions ◽  
Postcritically Finite ◽  
One To One ◽  
Complex Exponential

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z)\exp (q(z))$ for $p(z)$, $q(z)$ polynomials and $\exp (z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Haïssinsky.

Sign in / Sign up

Export Citation Format

Share Document