Geodesic
Recurrence of entire transcendental functions with simple post-singular sets
Jan-Martin Hemke1
1 Mathematisches Institut der Christian-Albrechts-Universität zu Kiel Ludwig-Meyn-Str. 4, 24118 Kiel, Germany
Fundamenta Mathematicae, Tome 187 (2005) no. 3, pp. 255-289

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study how the orbits of the singularities of the inverse of a meromorphic function determine the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide whether the function is recurrent or not. In the case that the Julia set is not the entire plane we also obtain estimates for the measure of the Julia set.
DOI : 10.4064/fm187-3-4
Keywords: study orbits singularities inverse meromorphic function determine dynamics its julia set least set lebesgue measure zero concentrate family entire transcendental functions only finitely many singularities inverse counting multiplicity which either escape exponentially fast pre periodic these functions able decide whether function recurrent the julia set entire plane obtain estimates measure julia set

Jan-Martin Hemke 1

1 Mathematisches Institut der Christian-Albrechts-Universität zu Kiel Ludwig-Meyn-Str. 4, 24118 Kiel, Germany 
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Jan-Martin Hemke. Recurrence of entire transcendental functions
 with simple post-singular sets. Fundamenta Mathematicae, Tome 187 (2005) no. 3, pp. 255-289. doi: 10.4064/fm187-3-4

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