Publication Cover
Dynamical Systems
An International Journal
Volume 39, 2024 - Issue 1
77
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On the distality and expansivity of certain maps on spheres

, &
Pages 166-181 | Received 10 Jan 2023, Accepted 01 Aug 2023, Published online: 03 Sep 2023

References

  • H. Abels, Distal affine transformation group, J. Reine Angew. Math. 299 (1978), pp. 294–300.
  • H. Abels, Distal automorphism groups of lie groups, J. Reine Angew. Math. 329 (1981), pp. 82–87.
  • J. Auslander and Y. Katznelson, Continuous maps of the circle without periodic points, Israel J. Math. 32(4) (1979), pp. 375–381.
  • M. Choudhuri and C.R.E. Raja, Nilpotent lie groups and hyperbolic automorphisms, Arch Math. (Basel) 115(3) (2020), pp. 247–255.
  • R. Ellis, Distal transformation groups, Pacific J. Math. 8(3) (1958), pp. 401–405.
  • H. Furstenberg, The structure of distal flows, Amer. J. Math. 85(3) (1963), pp. 477–515.
  • Michael-Robert Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. 49(1) (1979), pp. 5–233.
  • K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math. 27 (1990), pp. 117–162.
  • J.F. Jakobsen and W.R. Utz, The non-existence of expansive homeomorphisms on a closed 2-cell, Pacific J. Math. 10(4) (1960), pp. 1319–1321.
  • J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Bras. Math. (N.S.) 20(1) (1989), pp. 113–133.
  • N. G. Markley, Homeomorphisms of the circle without periodic points, Proc. London Math. Soc. (3), 20(4) (1970), pp. 688–698.
  • C.C. Moore, Distal affine transformation groups, Amer. J. Math. 90(3) (1968), pp. 733–751.
  • H. Poincaŕe, Mémoire sur les courbes définies par uneéquation différentielle, I. J. Math. Pures Appl.ées, 3. série, 7, pp. 375–422 (1881); II. 8, pp. 51–186 (1882); III. 4. série, 1, pp. 167–244 (1885); IV. 2, pp. 151–217 (1886).
  • W. Reddy, The existence of expansive homeomorphisms on manifolds, Duke Math. J. 32(4) (1965), pp. 627–632.
  • C.R.E. Raja and R. Shah, Distal actions and shifted convolution property, Israel J. Math. 177(1) (2010), pp. 391–412.
  • C.R.E. Raja and R. Shah, Some properties of distal actions on locally compact groups, Ergodic Theory Dynam. Syst. 35 (2017), pp. 1–21. doi:10.1017/etds.2017.58
  • R. Shah, Orbits of distal actions on locally compact groups, J. Lie Theory 22 (2012), pp. 586–599.
  • R. Shah, Expansive automorphisms on locally compact groups, New York J. Math. 26 (2022), pp. 285–302.
  • R. Shah and A.K. Yadav, Dynamics of certain distal actions on spheres, Real Anal. Exchange 44(1) (2019), pp. 77–88.
  • R. Shah and A.K. Yadav, Distality of certain actions on p-adic spheres, J. Aust. Math. Soc. 109(2) (2020), pp. 250–261.
  • J. A. Walsh, The dynamics of circle homeomorphisms: A hands-on introduction, Math. Mag. 72(1) (1999), pp. 3–13.
  • M.C. Zdun, On conjugacy of homeomorphisms of the circle possessing periodic points, J. Math. Anal. Appl. 330(1) (2007), pp. 51–65.

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.