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Dynamics of annulus maps II: Periodic points for coverings

Volume 235 / 2016

Jorge Iglesias, Aldo Portela, Álvaro Rovella, Juliana Xavier Fundamenta Mathematicae 235 (2016), 257-276 MSC: Primary 37C25; Secondary 37B20, 37B45, 37E30, 37E45. DOI: 10.4064/fm89-6-2016 Published online: 8 July 2016

Abstract

Let $f$ be a covering map of the open annulus $A= S^1\times (0,1)$ of degree $d$, $|d| \gt 1$. Assume that $f$ preserves an essential (i.e not contained in a disk of $A$) compact subset $K$. We show that $f$ has at least the same number of periodic points in each period as the map $z^d$ on $S^1.$

Authors

  • Jorge IglesiasIMERL, Facultad de Ingeniería
    Montevideo, Uruguay
    e-mail
  • Aldo PortelaIMERL, Facultad de Ingeniería
    Montevideo, Uruguay
    e-mail
  • Álvaro RovellaCMAT, Facultad de Ciencias
    Montevideo, Uruguay
    e-mail
  • Juliana XavierIMERL, Facultad de Ingeniería
    Montevideo, Uruguay
    e-mail

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