Skip to main content
Log in

Dynamics of Bohr almost periodic motions of topological abelian semigroups

  • Research Article
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

We study the topological and ergodic dynamics of Bohr almost periodic motions of a topological abelian semigroup acting continuously on a compact metric space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chen, B., Dai, X.: On uniformly recurrent motions of topological semigroup actions. Discret. Contin. Dyn. Syst. 36, 2931–2944 (2016)

    MATH  MathSciNet  Google Scholar 

  2. Dai, X.: Integral expressions of Lyapunov exponents for autonomous ordinary differential systems. Sci. in China Ser. A: Math. 52, 195–216 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dai, X.: Optimal state points of the subadditive ergodic theorem. Nonlinearity 24, 1565–1573 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  4. Egawa, J.: A characterization of regularly almost periodic minimal flows. Proc. Japan Acad. Ser. A 71, 225–228 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton (1981)

    Book  MATH  Google Scholar 

  6. Gottschalk, W.H., Hedlund, G.A.: Topological Dynamics. Amer. Math. Soc. Coll. Publ., Vol. 36, Amer. Math. Soc., Providence, R.I., (1955)

  7. del Junco, A., Rosenblatt, J.: Counterexamples in ergodic theory and number theory. Math. Ann. 245, 185–197 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lindenstrauss, E.: Pointwise theorems for amenable groups. Invent. Math. 146, 259–295 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Miller, A., Rosenblatt, J.: Characterizations of regular almost periodicity in compact minimal abelian flows. Trans. Amer. Math. Soc. 356, 4909–4929 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Nemytskii, V.V., Stepanov, V.V.: Qualitative theory of differential equations. Princeton University Press, Princeton (1960)

    MATH  Google Scholar 

  11. Royden, H.L.: Real analysis, 3rd edn. MacMillan, NY (1988)

    MATH  Google Scholar 

  12. Stepanov, V.V., Tychonoff, A.: Über die Räume der fastperiodischen Funktionen. Recueil Mathématique, Nouvelle Série 41, 166–178 (1934)

    MATH  Google Scholar 

Download references

Acknowledgments

This work was partly supported by National Natural Science Foundation of China grant \(\#\)11431012, 11271183 and PAPD of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiongping Dai.

Additional information

Communicated by Anthony To-Ming Lau.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, X. Dynamics of Bohr almost periodic motions of topological abelian semigroups. Semigroup Forum 95, 303–313 (2017). https://doi.org/10.1007/s00233-016-9809-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-016-9809-6

Keywords

Navigation