Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 248413, 8 pages
Research Article

On the Structure of Brouwer Homeomorphisms Embeddable in a Flow

Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Cracow, Poland

Received 10 May 2012; Accepted 25 July 2012

Academic Editor: Krzysztof Cieplinski

Copyright © 2012 Zbigniew Leśniak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Nakayama, “Limit sets and square roots of homeomorphisms,” Hiroshima Mathematical Journal, vol. 26, no. 2, pp. 405–413, 1996. View at Google Scholar
  2. L. E. J. Brouwer, “Beweis des ebenen Translationssatzes,” Mathematische Annalen, vol. 72, no. 1, pp. 37–54, 1912. View at Publisher · View at Google Scholar
  3. M. Brown, E. E. Slaminka, and W. Transue, “An orientation preserving fixed point free homeomorphism of the plane which admits no closed invariant line,” Topology and its Applications, vol. 29, no. 3, pp. 213–217, 1988. View at Publisher · View at Google Scholar
  4. E. W. Daw, “A maximally pathological Brouwer homeomorphism,” Transactions of the American Mathematical Society, vol. 343, no. 2, pp. 559–573, 1994. View at Publisher · View at Google Scholar
  5. P. Le Calvez and A. Sauzet, “Une démonstration dynamique du théorème de translation de Brouwer,” Expositiones Mathematicae, vol. 14, no. 3, pp. 277–287, 1996. View at Google Scholar
  6. T. Homma and H. Terasaka, “On the structure of the plane translation of Brouwer,” Osaka Journal of Mathematics, vol. 5, pp. 233–266, 1953. View at Google Scholar
  7. S. A. Andrea, “On homoeomorphisms of the plane which have no fixed points,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 30, pp. 61–74, 1967. View at Google Scholar
  8. Z. Leśniak, “On an equivalence relation for free mappings embeddable in a flow,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 7, pp. 1911–1915, 2003. View at Publisher · View at Google Scholar
  9. Z. Leśniak, “On parallelizability of flows of free mappings,” Aequationes Mathematicae, vol. 71, no. 3, pp. 280–287, 2006. View at Publisher · View at Google Scholar
  10. H. Nakayama, “On dimensions of non-Hausdorff sets for plane homeomorphisms,” Journal of the Mathematical Society of Japan, vol. 47, no. 4, pp. 789–793, 1995. View at Publisher · View at Google Scholar
  11. N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer, New York, NY, USA, 1970.
  12. Z. Leśniak, “On maximal parallelizable regions of flows of the plane,” International Journal of Pure and Applied Mathematics, vol. 30, no. 2, pp. 151–156, 2006. View at Google Scholar
  13. Z. Leśniak, “On a decomposition of the plane for a flow of free mappings,” Publicationes Mathematicae Debrecen, vol. 75, no. 1-2, pp. 191–202, 2009. View at Google Scholar
  14. Z. Leśniak, “On boundaries of parallelizable regions of flows of free mappings,” Abstract and Applied Analysis, vol. 2007, Article ID 31693, 8 pages, 2007. View at Publisher · View at Google Scholar
  15. F. Béguin and F. Le Roux, “Ensemble oscillant d'un homéomorphisme de Brouwer, homéomorphismes de Reeb,” Bulletin de la Société Mathématique de France, vol. 131, no. 2, pp. 149–210, 2003. View at Google Scholar
  16. P. Hartman, Ordinary Differential Equations, vol. 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 2002. View at Publisher · View at Google Scholar
  17. S. N. Elaydi, Discrete Chaos, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2nd edition, 2008.
  18. F. Le Roux, “Il n'y a pas de classification borélienne des homéomorphismes de Brouwer,” Ergodic Theory and Dynamical Systems, vol. 21, no. 1, pp. 233–247, 2001. View at Publisher · View at Google Scholar
  19. F. Le Roux, “Classes de conjugaison des flots du plan topologiquement équivalents au flot de Reeb,” Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, vol. 328, no. 1, pp. 45–50, 1999. View at Publisher · View at Google Scholar