Repelling periodic points and landing of rays for post-singularly bounded exponential maps

Anna Miriam Benini[1]; Mikhail Lyubich[2]

  • [1] Universita’ di Tor Vergata Dipartimento di matematica Via della Ricerca Scientifica 001133 Roma (Italy)
  • [2] Stony Brook University Department of Mathematics Stony Brook, NY 11794-3651 (USA)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 4, page 1493-1520
  • ISSN: 0373-0956

Abstract

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We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.

How to cite

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Benini, Anna Miriam, and Lyubich, Mikhail. "Repelling periodic points and landing of rays for post-singularly bounded exponential maps." Annales de l’institut Fourier 64.4 (2014): 1493-1520. <http://eudml.org/doc/275613>.

@article{Benini2014,
abstract = {We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.},
affiliation = {Universita’ di Tor Vergata Dipartimento di matematica Via della Ricerca Scientifica 001133 Roma (Italy); Stony Brook University Department of Mathematics Stony Brook, NY 11794-3651 (USA)},
author = {Benini, Anna Miriam, Lyubich, Mikhail},
journal = {Annales de l’institut Fourier},
keywords = {rigidity; accessibility; exponential maps; combinatorics; polynomials},
language = {eng},
number = {4},
pages = {1493-1520},
publisher = {Association des Annales de l’institut Fourier},
title = {Repelling periodic points and landing of rays for post-singularly bounded exponential maps},
url = {http://eudml.org/doc/275613},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Benini, Anna Miriam
AU - Lyubich, Mikhail
TI - Repelling periodic points and landing of rays for post-singularly bounded exponential maps
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 4
SP - 1493
EP - 1520
AB - We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.
LA - eng
KW - rigidity; accessibility; exponential maps; combinatorics; polynomials
UR - http://eudml.org/doc/275613
ER -

References

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