47
Views
0
CrossRef citations to date
0
Altmetric
Articles

On families of invariant lines of a Brouwer homeomorphism

ORCID Icon
Pages 1363-1371 | Received 27 Feb 2019, Accepted 27 Jun 2019, Published online: 11 Jul 2019

References

  • S.A. Andrea, On homeomorphisms of the plane which have no fixed points, Abh. Math. Sem. Hamburg 30 (1967), pp. 61–74. doi: 10.1007/BF02993992
  • F. Béguin and F. LeRoux, Ensemble oscillant d'un homéomorphisme de Brouwer, homéomorphismes de Reeb, Bull. Soc. Math. France 131(2) (2003), pp. 149–210. doi: 10.24033/bsmf.2439
  • L.E.J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann. 72 (1912), pp. 37–54. doi: 10.1007/BF01456888
  • M. Brown, Fundamental regions of planar homeomorphisms, Contemp. Math. 117 (1991), pp. 49–56. doi: 10.1090/conm/117/1112802
  • E.W. Daw, A maximally pathological Brouwer homeomorphism, Trans. Amer. Math. Soc. 343 (1994), pp. 559–573. doi: 10.1090/S0002-9947-1994-1173856-7
  • T. Homma and H. Terasaka, On the structure of the plane translation of Brouwer, Osaka. Math. J. 5 (1953), pp. 233–266.
  • F. LeRoux, A.G. O'Farrell, M. Roginskaya, and I. Short, Flowability of plane homeomorphisms, Ann. Inst. Fourier 62(2) (2012), pp. 619–639. doi: 10.5802/aif.2689
  • Z. Leśniak, On an equivalence relation for free mappings embeddable in a flow, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13(7) (2003), pp. 1911–1915. doi: 10.1142/S0218127403007746
  • Z. Leśniak, On parallelizability of flows of free mappings, Aequationes Math. 71(3) (2006), pp. 280–287. doi: 10.1007/s00010-005-2808-4
  • Z. Leśniak, On fractional iterates of a Brouwer homeomorphism embeddable in a flow, J. Math. Anal. Appl. 366(1) (2010), pp. 310–318. doi: 10.1016/j.jmaa.2009.12.033
  • Z. Leśniak, On the structure of Brouwer homeomorphisms embeddable in a flow, Abstr. Appl. Anal. 2012 (2012), 8 pp. Article ID 248413.
  • Z. Leśniak, On properties of the set of invariant lines of a Brouwer homeomorphism, J. Differ. Equ. Appl. 24 (2018), pp. 746–752. doi: 10.1080/10236198.2017.1337107
  • H. Nakayama, A non flowable plane homeomorphism whose non Hausdorff set consists of two disjoint lines, Houston J. Math. 21(3) (1995), pp. 569–572.
  • H. Nakayama, Limit sets and square roots of homeomorphisms, Hiroshima Math. J. 26 (1996), pp. 405–413. doi: 10.32917/hmj/1206127370

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.