Ir al contenido

Documat


A Generalization of the Brouwer Plane Translation Theorem

  • Jim Wiseman [1]
    1. [1] Agnes Scott College

      Agnes Scott College

      Estados Unidos

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen
    • We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.

  • Referencias bibliográficas
    • 1. Brouwer, L.E.J.: Beweis des ebenen translationssatzes. Math. Ann. 72(1), 37–54 (1912)
    • 2. Brown, M.: A new proof of Brouwer’s lemma on translation arcs. Houst. J. Math. 10(1), 35–41 (1984)
    • 3. Das, Tarun, Lee, Keonhee, Richeson, David, Wiseman, Jim: Spectral decomposition for topologically Anosov homeomorphisms on noncompact and...
    • 4. Edward, E., Slaminka, A.: Brouwer translation theorem for free homeomorphisms. Trans. Amer. Math. Soc. 306(1), 277–291 (1988)
    • 5. Fathi, Albert: An orbit closing proof of Brouwer’s lemma on translation arcs. Enseign. Math. 33(3–4), 315–322 (1987)
    • 6. Franks, John: Generalizations of the Poincaré-Birkhoff theorem. Ann. of Math. 128(1), 139–151 (1988)
    • 7. Franks, J: A variation on the Poincaré-Birkhoff theorem, Hamiltonian dynamical systems, pp. 111–117. Boulder, CO (1987). 1988
    • 8. Franks, John: A new proof of the Brouwer plane translation theorem. Ergod. Theory Dyn. Syst. 12(2), 217–226 (1992)
    • 9. Guillou, Lucien: Théorème de translation plane de Brouwer et généralisations du théorème de PoincaréBirkhoff. Topology 33(2), 331–351 (1994)
    • 10. Hurley, Mike: Chain recurrence and attraction in noncompact spaces. Ergod. Theory Dyn. Syst. 11(4), 709–729 (1991)
    • 11. Le Calvez, Patrice, Sauzet, Alain: Une démonstration dynamique du théorème de translation de Brouwer. Exposition. Math. 14(3), 277–287...
    • 12. Mai, J., Yan, K., Zeng, F.: Orientation preserving homeomorphisms of the plane having BP-chain recurrent points. arXiv:2404.10247v1 (2024)
    • 13. Ziemer, William P.: Modern real analysis, Graduate Texts in Mathematics, vol. 278, 2nd edn. Springer, Berlin (2017). (With contributions...

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno