Universal bounds on the entropy of toroidal attractors

• Pedro Montealegre-Macías ^[1] ; Jaime J. Sánchez-Gabites ^[2]
  1. [1] Universidad de Castilla-La Mancha

     Universidad de Castilla-La Mancha

     Ciudad Real, España

     
  2. [2] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 5, 2024, págs. 1953-1988
• Idioma: inglés
• DOI: 10.4171/RMI/1496
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• Resumen

  • A toroidal set is a compactum K⊆R 3 which has a neighbourhood basis of solid tori. We study the topological entropy of toroidal attractors K, bounding it from below in terms of purely topological properties of K. In particular, we show that for a toroidal set K, either any smooth attracting dynamics on K has an entropy at least log2, or (up to continuation) K admits smooth attracting dynamics which are stationary (hence with a zero entropy).