Polynomial entropy on regular curves

• Đorić, Maša ^[2] ; Katić, Jelena ^[1]
  1. [1] University of Belgrade

     University of Belgrade

     Serbia

     
  2. [2] Mathematical Institute of the Serbian Academy of Sciences and Arts
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.4995/agt.25695
• Enlaces
  • Texto completo
• Resumen

  • We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a rigidity result for homeomorphisms on local dendrites (and therefore on graphs and dendrites): their polynomial entropy is either zero or one.

• Referencias bibliográficas
  • J. Bohorquez, On the entropy of the continuum hyperspace map, PhD thesis (Brasil, 2017).
  • M. Đorić, J. Katić, and B. Lasković, On polynomial entropy of induced maps on symmetric products, Acta Math. Hungar. 171 (2023), 334-347....
  • J. B. Gomes and M. J. D. Carneiro, Polynomial entropy for interval maps and lap number, Qual. Theory Dyn. Syst. 20 (2021), 21. https://doi.org/10.1007/s12346-021-00456-y
  • F. Grycan-Gérard and J. P. Marco, Polynomial entropy and polynomial torsion for fibered systems, Regul. Chaotic Dyn. 28, no. 4-5 (2023), 613-627....
  • H. Kato, Topological entropy of maps on regular curves, Topology Appl. 154 (2007), 1027-1031. https://doi.org/10.1016/j.topol.2006.10.011
  • D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos, Solitons & Fractals 33, no. 1 (2007),...
  • C. Labrousse, Polynomial entropy for the circle homeomorphisms and for $C^1$ nonvanishing vector fields on $mathbb{T}^2$, arXiv:1311.0213.
  • J. P. Marco, Dynamical complexity and symplectic integrability, arXiv:0907.5363v1.
  • J. P. Marco, Polynomial entropies and integrable Hamiltonian systems, Regul. Chaotic Dyn. 18, no. 6 (2013), 623-655. https://doi.org/10.1134/S1560354713060051
  • S. B. Nadler, Jr., Continuum theory. An introduction, Marcel Dekker, New York (1992).
  • I. Naghmouchi, Dynamics of homeomorphisms of regular curves, Colloquium Mathematicum 162 (2020), 263-277. https://doi.org/10.4064/cm7825-9-2019
  • S. Roth, Z. Roth, and L. Snoha, Rigidity and flexibility of polynomial entropy, Adv. Math. 443 (2024), 109591. https://doi.org/10.1016/j.aim.2024.109591
  • A. H. Salem, H. Hattab, and T. Rejeiba, Equicontinuous local dendrite maps, Appl. Gen. Topol. 22, no. 1 (2021), 67-77. https://doi.org/10.4995/agt.2021.13446
  • G. T. Seidler, The topological entropy of homeomorphisms on one-dimensional continua, Proceedings of the American Mathematical Society 108...
  • P. Sharma and A. Nagar, Topological dynamics on hyperspaces, Appl. Gen. Topol. 11, no. 1 (2010), 1-19. https://doi.org/10.4995/agt.2010.1724