Dynamical properties of some classes of entire functions

A. Eremenko; M. Yu Lyubich

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 4, page 989-1020
  • ISSN: 0373-0956

Abstract

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The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.

How to cite

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Eremenko, A., and Lyubich, M. Yu. "Dynamical properties of some classes of entire functions." Annales de l'institut Fourier 42.4 (1992): 989-1020. <http://eudml.org/doc/74982>.

@article{Eremenko1992,
abstract = {The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.},
author = {Eremenko, A., Lyubich, M. Yu},
journal = {Annales de l'institut Fourier},
keywords = {dynamics; periodic points; entire function; Julia set; structural stability},
language = {eng},
number = {4},
pages = {989-1020},
publisher = {Association des Annales de l'Institut Fourier},
title = {Dynamical properties of some classes of entire functions},
url = {http://eudml.org/doc/74982},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Eremenko, A.
AU - Lyubich, M. Yu
TI - Dynamical properties of some classes of entire functions
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 4
SP - 989
EP - 1020
AB - The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.
LA - eng
KW - dynamics; periodic points; entire function; Julia set; structural stability
UR - http://eudml.org/doc/74982
ER -

References

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