The analytic fixed point function II

Diego Mejía; Christian  Pommerenke

Publicado

2006-01-01

The analytic fixed point function II

Palabras clave:

Fixed point function, Coefficients, Bürmann-Lagrange, Asymptotics, Equilibrium, First return, Branching process, 2000 Mathematics Subject Classification, Primary: 30B10, Secondary: 60F99, 60J80 (en)

Descargas

PDF (English)

Autores/as

Diego Mejía Universidad Nacional de Colombia (Sede Medellín)
Christian Pommerenke Technische Universität, Berlin

Resumen (en)

Abstract. Let ϕ be analytic in the unit disk ⅅ and let ϕ (ⅅ) ⊂ ⅅ, ϕ (0). Then w = ƶ/ϕ (ƶ) has an analytic inverse ƶ = ƒ (w) for w ϵ ⅅ, the fixed point function. This paper studies the case that ϕ (1) = ϕ'(1) = 1 with a growth condition for ϕ"(χ) and determines the asymptotic behaviour of various combinations of the coefficients of ϕ connected with ƒ. The results can be interpreted in various contexts of probability theory.

Referencias

[AtNe72] K. B. Athreya & P. E. Ney, Branching processes, Springer, Berlin, 1972.

[Fe68] W. Feller, An introduction to probability theory and its applications I, John Wiley & Sons, New York, 1968.

[Gä77] J. Gärtner, On large deviations from the invariant measure, Theory Probab. Appl. 22 (1977), 24-39.

[KaNa94] A. V. Karpenko & V. Nagaev, Limit theorems for the total number of descendants for the Galton-Watson branching process, Theory Probab. Appl. 38 (1994), 433-455.

[MePo05] D. Mejia & Ch. Pommerenke, The analytic fixed point function in the disk, Comput. Methods Fund. Theory, 5 no. 2 (2005), 275-299.

[Pe75] V. V. Petrov, Sums of independent random variables, Springer, Berlin, 1975.

[PoSz25] G. Pöya & G. Szegö, Aufgaben und Lehrsätze aus der Analysis I, Springer, Berlin, 1925. [Po92] Ch. Pommerenke, Boundary behaviour of conformal maps, Springer, Berlin, 1992.

Cómo citar

APA

Mejía, D. y Pommerenke, C. (2006). The analytic fixed point function II. Revista Colombiana de Matemáticas, 40(1), 39–52. https://revistas.unal.edu.co/index.php/recolma/article/view/94669

ACM

[1]

Mejía, D. y Pommerenke, C. 2006. The analytic fixed point function II. Revista Colombiana de Matemáticas. 40, 1 (ene. 2006), 39–52.

ACS

(1)

Mejía, D.; Pommerenke, C. The analytic fixed point function II. rev.colomb.mat 2006, 40, 39-52.

ABNT

MEJÍA, D.; POMMERENKE, C. The analytic fixed point function II. Revista Colombiana de Matemáticas, [S. l.], v. 40, n. 1, p. 39–52, 2006. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94669. Acesso em: 22 ene. 2025.

Chicago

Mejía, Diego, y Christian Pommerenke. 2006. «The analytic fixed point function II». Revista Colombiana De Matemáticas 40 (1):39-52. https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Harvard

Mejía, D. y Pommerenke, C. (2006) «The analytic fixed point function II», Revista Colombiana de Matemáticas, 40(1), pp. 39–52. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94669 (Accedido: 22 enero 2025).

IEEE

[1]

D. Mejía y C. Pommerenke, «The analytic fixed point function II», rev.colomb.mat, vol. 40, n.º 1, pp. 39–52, ene. 2006.

MLA

Mejía, D., y C. Pommerenke. «The analytic fixed point function II». Revista Colombiana de Matemáticas, vol. 40, n.º 1, enero de 2006, pp. 39-52, https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Turabian

Mejía, Diego, y Christian Pommerenke. «The analytic fixed point function II». Revista Colombiana de Matemáticas 40, no. 1 (enero 1, 2006): 39–52. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94669.

Vancouver

1.

Mejía D, Pommerenke C. The analytic fixed point function II. rev.colomb.mat [Internet]. 1 de enero de 2006 [citado 22 de enero de 2025];40(1):39-52. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94669