One-parameter semigroups of analytic functions, fixed points and the Koenigs function

2011 ◽  
Vol 202 (7) ◽  
pp. 971-1000 ◽  
Author(s):  
Victor V Goryainov ◽  
Olga S Kudryavtseva
Keyword(s):  
Fixed Points ◽  
Analytic Functions ◽  
Koenigs Function

Linearization of holomorphic germs with quasi-parabolic fixed points

2008 ◽  
Vol 28 (3) ◽  
pp. 979-986 ◽  
Author(s):  
FENG RONG
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Analytic Functions ◽  
Classical Result ◽  
Linear Part ◽  
Analytic Form ◽  
Moscow Math ◽  
Parabolic Fixed Point

AbstractLet f be a germ of a holomorphic diffeomorphism of $\mathbb {C}^n$ with the origin O being a quasi-parabolic fixed point, i.e. the spectrum of dfO consists of 1 and e2iπθj with $\theta _j\in \mathbb {R}\!\setminus \!\mathbb {Q}$. We show that f is locally holomorphically conjugated to its linear part, if f is of some particular form and its eigenvalues satisfy certain arithmetic conditions. When the spectrum of dfO does not consist of any 1’s, this is the classical result of Siegel [C. L. Siegel. Iteration of analytic functions. Ann. of Math.43 (1942), 607–612] and Brjuno [A. D. Brjuno. Analytic form of differential equations. Trans. Moscow Math. Soc.25 (1971), 131–288; 26 (1972), 199–239].

scholarly journals A new class of multivalent analytic functions defined by the Hadamard product

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Fixed Points ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Partial Sums ◽  
New Class

AbstractThe object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.

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.

scholarly journals Analytic functions over valued fields

1990 ◽  
Vol 13 (2) ◽  
pp. 247-252
Author(s):  
R. Bhaskaran ◽  
V. Karunakaran
Keyword(s):  
Unit Ball ◽  
Fixed Points ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Ball ◽  
Valued Fields ◽  
Complete Field ◽  
Necessary And Sufficient

LetKbe a non-archimedean, non-trivially (rank 1) valued complete field.B,B0denote the closed and open unit ball ofKrespectively. Necessary and sufficient conditions for analytic functions defined onB,B0with values inKto be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

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