Ir al contenido

Documat


A Note on Homeo-Product-Minimality

  • Autores: J.P. Boronski, Magdalena Forys-Krawiec
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
  • Idioma: inglés
  • Enlaces
  • Resumen
    • A compact space Y is called homeo-product-minimal if given any minimal system (X, T ), it admits a homeomorphism S : Y → Y , such that the product system (X × Y , T × S) is minimal. We show that a large class of cofrontiers is homeo-productminimal. This class contains Bing’s pseudo-circle, answering a question of Dirbák et al. (Trans Am Math Soc 375:6453–6506, 2022).

  • Referencias bibliográficas
    • 1. Bing, R.H.: Concerning hereditarily indecomposable continua. Pac. J. Math. 1, 43–51 (1951)
    • 2. Béguin, F., Crovisier, S., Jäger, T.: A dynamical decomposition of the torus into pseudo-circles. In: Modern Theory of Dynamical Systems:...
    • 3. Boro ´nski, J.P., Oprocha, P.: Rotational chaos and strange attractors on the 2-torus. Math. Z. 279, 689–702 (2015)
    • 4. Boro ´nski, J., Clark, A., Oprocha, P.: New exotic minimal sets from pseudo-suspensions of Cantor systems. J. Dyn. Differ. Equ. (2023)....
    • 5. Boro ´nski, J., Clark, A., Oprocha, P.: A compact minimal space Y such that its square YíY is not minimal. Adv. Math. 335, 261–275 (2018)
    • 6. Boro ´nski, J.P., Kennedy, J., Liu, X.-C., Oprocha, P.: Minimal non-invertible maps on the pseudo-circle. J. Dyn. Differ. Equ. 33(4), 1897–1916...
    • 7. Brown,M.: Continuous collections of higher dimensional hereditarily indecomposable continua. Thesis (Ph.D.), The University of Wisconsin,...
    • 8. Chéritat, A.: Relatively compact Siegel disks with non-locally connected boundaries. Math. Ann. 349, 529–542 (2011)
    • 9. Cinˇ ˇ c, J., Oprocha, P.: Parametrized family of annular homeomorphisms with pseudo-circle attractors. arXiv:2305.06467
    • 10. Dirbák, M., Snoha, L., Špitalský, V.: Minimal direct products. Trans. Am. Math. Soc. 375, 6453–6506 (2022)
    • 11. Downarowicz, T., Snoha, L., Tywoniuk, D.: Minimal spaces with cyclic group of homeomorphisms. J. Dyn. Differ. Eqn. 29, 243–257 (2017)
    • 12. Fearnley, L.: The pseudo-circle is unique. Trans. Am. Math. Soc. 149, 45–64 (1970)
    • 13. Handel, M.: A pathological area preserving C∞ diffeomorphism of the plane. Proc. Am. Math. Soc. 86, 163–168 (1982)
    • 14. Kennedy, J., Rogers, J.T.: Orbits of the pseudocircle. Trans. Am. Math. Soc. 296(1), 327–340 (1986)
    • 15. Kennedy, J., Yorke, J.A.: Pseudocircles in dynamical systems. Trans. Am. Math. Soc. 343, 349–366 (1994)
    • 16. Kennedy, J., Yorke, J.A.: Bizarre topology is natural in dynamical systems. Bull. Am. Math. Soc. 32, 309–316 (1995)
    • 17. Kennedy, J., Yorke, J.A.: Pseudocircles, diffeomorphisms and perturbable dynamical systems. Ergod. Theory Dyn. Syst. 16, 1031–1057 (1996)
    • 18. Lewis, W.: Pseudo-arcs and connectedness in homeomorphism groups. Proc. Am. Math. Soc. 142, 745–748 (1983)
    • 19. Kolyada, S., Snoha, L., Trofimchuk, S.: Minimal sets of fibre-preserving maps in graph bundles. Math. Z. 278, 575–614 (2014)
    • 20. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. Wiley, New York (1974)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno