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Gallardo Gutiérrez, Eva A. and Nieminen, Pekka J.
(2015)
*The Linear Fractional Model Theorem and Aleksandrov-Clark measures.*
Journal of the London Mathematical Society. Second Series, 91
(2).
pp. 596-608.
ISSN 0024-6107

PDF
Restringido a Repository staff only 213kB |

Official URL: http://jlms.oxfordjournals.org/content/91/2/596.abstract

## Abstract

A remarkable result by Denjoy and Wolff states that every analytic self-map. of the open unit disc D of the complex plane, except an elliptic automorphism, has an attractive fixed point to which the sequence of iterates {phi(n)}(n >= 1) converges uniformly on compact sets: if there is no fixed point in D, then there is a unique boundary fixed point that does the job, called the Denjoy-Wolff point. This point provides a classification of the analytic self-maps of D into four types: maps with interior fixed point, hyperbolic maps, parabolic automorphism maps and parabolic non-automorphism maps. We determine the convergence of the Aleksandrov-Clark measures associated to maps falling in each group of such classification

Item Type: | Article |
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Uncontrolled Keywords: | Analytic-Functions; Unit disk; Iteration |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 34302 |

Deposited On: | 01 Dec 2015 08:43 |

Last Modified: | 02 Dec 2015 11:28 |

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