scholarly journals Correlations between zeros and critical points of random analytic functions

2019 ◽  
Vol 371 (8) ◽  
pp. 5247-5265
Author(s):  
Renjie Feng
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Random Analytic Functions ◽  
Correlations Between Zeros

Multivalent and Meromorphic Functions of Bounded Boundary Rotation

1975 ◽  
Vol 27 (1) ◽  
pp. 186-199 ◽  
Author(s):  
Ronald J. Leach
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,andWe note that (1.1) implies that / has precisely p — 1 critical points in U.

Extremal Points, Critical Points, and Saddle Points of Analytic Functions

2007 ◽  
Vol 114 (6) ◽  
pp. 540-546 ◽  
Author(s):  
Joseph Bak ◽  
Pisheng Ding ◽  
Donald Newman
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Saddle Points ◽  
Extremal Points

Hyperplane Singularities of Analytic Functions of Several Complex Variables

1997 ◽  
Vol 4 (2) ◽  
pp. 163-184
Author(s):  
M. Shubladze
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Algebraic Expression ◽  
Isolated Singularities ◽  
Milnor Fibre ◽  
New Class

Abstract A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.

scholarly journals On boundary critical points for semigroups of analytic functions

2006 ◽  
Vol 98 (1) ◽  
pp. 125 ◽  
Author(s):  
M. D. Contreras ◽  
S. Díaz-Madrigal ◽  
Ch. Pommerenke
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
Critical Points ◽  
Analytic Functions ◽  
Infinitesimal Generators ◽  
Contact Points ◽  
Angular Derivatives ◽  
Boundary Fixed Points ◽  
The Relationship ◽  
New Inequalities

We analyze the relationship between boundary fixed points of semigroups of analytic functions and boundary critical points of their infinitesimal generators. As a consequence, we show two new inequalities for analytic self-maps of the unit disk. The first one is about angular derivatives at fixed points of functions belonging to semigroups of analytic functions. The second one deals with angular derivatives at contact points of arbitrary analytic functions from the unit disk into itself.

Sign in / Sign up

Export Citation Format

Share Document