Advanced search
Publication Cover
Dynamical Systems
An International Journal
Volume 37, 2022 - Issue 1
Submit an article Journal homepage
68
Views
1
CrossRef citations to date
0
Altmetric
Research Article

An operator theoretical approach to the sequence entropy of dynamical systems

M. RahimiDepartment of Mathematics, Faculty of Science, University of Qom, Qom, IranCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0003-0856-4559
ORCID Icon &
M. Mohammadi AnjedaniDepartment of Mathematics, Faculty of Science, University of Qom, Qom, Iran
Pages 56-65 | Received 12 May 2021, Accepted 26 Oct 2021, Published online: 26 Nov 2021

References

  • Adler R. L., Konheim A. G. and McAndrew M. H., Topological entropy, Trans. Amer. Math. Soc 114 (1965), pp. 309–319.
  • Cánovas J.S., On topological sequence entropy of circle maps, Appl. Gen. Topol. Univ. Politécnica De Valencia 114 (1965), pp. 309–319.
  • Cánovas J.S., New results on entropy, sequence entropy and related topics, Ph.D. Thesis, Universidad de Murcia, 2000.
  • Cánovas J.S., Topological sequence entropy and chaos of star maps, Nonlinear Dyn. Syst. Theory5 (2005), pp. 1–8.
  • Cánovas J.S., Topological sequence entropy and topological dynamics of interval maps, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 14 (2007), pp. 47–54.
  • Cánovas J.S. and Jimémez López V., Computing explicitly topological sequence entropy: The unimodal case, Ann. Inst. Fourier (Grenoble) 52 (2002), pp. 1093–1133.
  • Conway J.B., A course in functional analysis, 2nd ed., Springer-Verlag, New York, 1990.
  • Goodman T.N.T., Topological sequence entropy, Proc. Lond. Math. Soc. 29 (1974), pp. 331–350.
  • Hric R., Topological sequence entropy for maps of the circle, Comment Math. Univ. Carolin. 41 (2000), pp. 53–59.
  • Jiménez López V., An explicit description of all scrambled sets of weakly unimodal functions of type 2∞, Real. Anal. Exch. 21 (1995/1996), pp. 1–26.
  • Kolmogorov A.N., New metric invariant of transitive dynamical systems and endomorphisms of Lebesgue spaces, Dokl. Russ. Acad. Sci. 119, N5 (1958), pp. 861–864.
  • Kolyada S., Misiurewicz M. and Snoha L'., Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fund. Math. 160 (1999), pp. 161–181.
  • Kolyada S. and Snoha L'., Topological entropy of nonautonomous dynamical systems, Random Comp. Dyn. 4 (1996), pp. 205–233.
  • Kushnirenko A.G., On metric invariants of entroy type, Russ. Math. Surv. 22 (1967), pp. 53–61.
  • Lemanczycz M., The sequence entropy for morse shifts and some counterexamples, Studia Math. 82 (1985), pp. 221–241.
  • Newton D., On sequence entropy I, II, Math. Syst. Th. 4 (1970), pp. 119–125.
  • Pesin Ya., Characteristic Lyapunov exponents and smooth ergodic theory, Russ. Math. Surv. 32 (1977), pp. 54–114.
  • Rahimi M., A Spectral Representation for the Entropy of Topological Dynamical Systems, J. Dyn. Control. Syst. 27, 573–584 (2021). Available from: https://doi.org/https://doi.org/10.1007/s10883-020-09519-w.
  • Shannon C., A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948), pp. 623–656.
  • Walters P., An introduction to ergodic theory, Springer-Verlag New York, 1982.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.