Polynomial Entropy of Induced Maps of Circle and Interval Homeomorphisms

• Maša Doric ^[2] ; Jelena Katic ^[1]
  1. [1] University of Belgrade

     University of Belgrade

     Serbia

     
  2. [2] Matematicki institut SANU
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We compute the polynomial entropy of the induced maps on hyperspace for a homeomorphism f of an interval or a circle with finitely many non-wandering points. Also, we give a generalization for the case of an interval homeomorphism with an infinite non-wandering set.

• Referencias bibliográficas
  • 1. Acosta, G., Illanes, A., Méndez-Lango, H.: The transitivity of induced maps. Topology Appl. 156, 1013–1033 (2009)
  • 2. Arbieto, A., Bohorquez, J.: Shadowing, topological entropy and recurrence of induced Morse-Smale diffeomorphisms. arXiv:2203.13356 (2022)
  • 3. Artigue, A., Carrasco-Olivera, D., Monteverde, I.: Polynomial entropy and expansivity. Acta Math. Hungar. 152, 140–149 (2017)
  • 4. Banks, J.: Chaos for induced hyperspace map. Chaos Solitons Fract. 25, 681–685 (2005)
  • 5. Bauer, W., Sigmund, K.: Topological dynamics of transformations induced on the space of probability measures. Monatsh. Math. 79(2), 81–92...
  • 6. Bernard, P., Labrousse, C.: An entropic characterization on the flat metric on the two torus. Geom. Dedicata 180, 187–201 (2016)
  • 7. Borsuk, K., Ulam, S.: On symmetric products of topological spaces. Bull Amer. Math. Soc. 37, 875–882 (1931)
  • 8. Correa, J., de Paula, H.: Polynomial entropy of Morse–Smale diffeomorphisms on surfaces. arXiv:2203.08336v2 (2022)
  • 9. Daghar, A., Naghmouchi, I.: Entropy of induced maps of regular curves homeomorphisms. Chaos Solitons Fract. 157, 111988 (2022)
  • 10. Gomes, J.B., Carneiro, M.J.D.: Polynomial entropy for interval maps and lap number. Qual. Theory Dyn. Syst. 20(1), 1–16 (2021)
  • 11. Hauseux, L., Le Roux, F.: Entropie polynomiale des homémorphismes de Brouwer. Ann. Henri Lebesgue 2, 39–57 (2019)
  • 12. Hernández, P., Méndez, H.: Entropy of induced dendrite homeomorphisms. Topology Proc. 47, 191–205 (2016)
  • 13. Kati´c, J., Peri´c, M.: On the polynomial entropy for Morse gradient systems. Math. Slovaca 69(3), 611–624 (2019)
  • 14. Kwietniak, D., Oprocha, P.: Topological entropy and chaos for maps induced on hyperspaces. Chaos Solitons Fract. 33(1), 76–86 (2007)
  • 15. Labrousse, C.: Polynomial growth of the volume of balls for zero-entropy geodesic systems. Nonlinearity 25, 3049–3069 (2012)
  • 16. Labrousse, C.: Flat metrics are strict local minimizers for the polynomial entropy. Regul. Chaotic Dyn. 17, 47–491 (2012)
  • 17. Labrousse, C.: Polynomial entropy for the circle homeomorphisms and for C1 nonvanishing vector fields on T2. arXiv:1311.0213 (2013)
  • 18. Labrousse, C., Marco, J.P.: Polynomial entropies for Bott integrable Hamiltonian systems. Regul. Chaotic Dyn. 19, 374–414 (2014)
  • 19. Lampart, M., Raith, P.: Topological entropy for set valued maps. Nonlinear Anal. 73(6), 1533–1537 (2010)
  • 20. Marco, J.P.: Dynamical complexity and symplectic integrability. arXiv:0907.5363v1 (2009)
  • 21. Marco, J.P.: Polynomial entropies and integrable Hamiltonian systems. Regul. Chaotic Dyn. 18(6), 623–655 (2013)
  • 22. Robinson, C.: Dynamical Systems. Studies in Advanced Mathematics, CRC Press, Boca Raton (1995)
  • 23. Román-Flores, H.: A note on transitivity in set-valued discrete systems. Chaos Solitons Fract. 17(1), 99–104 (2003)
  • 24. Roth, S., Roth, Z., Snoha, L’.: Rigidity and flexibility of polynomial entropy. arXiv:2107.13695v1(2021)