<p>In this paper we present an alternative proof that the horseshoe map inherits the dynamical properties of the shift map by using the Cantor map and an equivalence relation defined on the Cantor sets on the unit rectangle.</p>

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Dynamical properties of the horseshoe map

  • Alejandro Cardona Zapata,
  • Oscar Iván Giraldo Galeano,
  • José Gregorio Rodríguez-Nieto

摘要

In this paper we present an alternative proof that the horseshoe map inherits the dynamical properties of the shift map by using the Cantor map and an equivalence relation defined on the Cantor sets on the unit rectangle.