Search Advanced

AIMS Mathematics

2017, Volume 2, Issue 1: 24-27. doi: 10.3934/Math.2017.1.24
Previous Article Next Article
Research article

Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points

  • Department of Mathematics, University of Wisconsin, Madison WI 53706, USA
  • Received: 29 November 2016 Accepted: 30 November 2016 Published: 16 December 2016

  • Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a closed convex cone $K\subset \mathbb{R}^{n}$ having nonempty interior. Let $T: X\approx X$ be an order-preserving homeomorphism. The following result is proved: Assume the set of periodic points of $T$ is dense in $X$, and $K$ is a polyhedron. Then $T$ is periodic.

    Citation: Morris W. Hirsch. Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points[J]. AIMS Mathematics, 2017, 2(1): 24-27. doi: 10.3934/Math.2017.1.24

    Related Papers:

  • Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a closed convex cone $K\subset \mathbb{R}^{n}$ having nonempty interior. Let $T: X\approx X$ be an order-preserving homeomorphism. The following result is proved: Assume the set of periodic points of $T$ is dense in $X$, and $K$ is a polyhedron. Then $T$ is periodic.


    加载中
    [1] R. Baire, Sur les fonctions de variables réelles, Ann. di Mat. 3 (1899), 1-123.
    [2] M. Hirsch and H. Smith, Monotone Dynamical Systems, Handbook of Differential Equations, volume 2, chapter 4. A. C?nada, P. Drabek & A. Fonda, editors. Elsevier North Holland, 2005.
    [3] S. Kaul, On pointwise periodic transformation groups, Proceedings of the American Mathematical Society 27 (1971), 391-394.
    [4] D. Montgomery, Pointwise periodic homeomorphisms, American Journal of Mathematics 59 (1937), 118-120.
    [5] E. Spanier, Algebraic Topology, McGraw Hill, 1966.
    [6] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, 1941.
    [7] R. Wilder, Topology of Manifolds, American Mathematical Society, 1949.
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(4576) PDF downloads(1056) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog