54
Views
0
CrossRef citations to date
0
Altmetric
Articles

The new notion of Bohl dichotomy for non-autonomous difference equations and its relation to exponential dichotomy

, &
Pages 626-658 | Received 01 Feb 2023, Accepted 04 Feb 2024, Published online: 14 Feb 2024

References

  • A. Babiarz, E. Barabanov, A. Czornik, A. Konyukh, M. Niezabitowsk, and A. Vaidzelevich, Relations between Bohl and general exponents, Discrete Contin. Dyn. Syst. Ser. A 37(10) (2017), pp. 5319–5335.
  • A. Babiarz, A. Czornik, and M. Niezabitowski, Relations between Bohl exponents and general exponent of discrete linear time-varying systems, J. Differ. Equ. Appl. 25(4) (2019), pp. 560–572.
  • E. Barabanov and E. Bekryaeva, Two generalized classes of exponentially dichotomous linear differential systems on the time half-line without uniform estimates for the solution norms I, Differ. Equ. 56(1) (2020), pp. 14–28.
  • L. Barreira and C. Valls, Robustness of dichotomies and trichotomies for difference equations, Port. Math. 71(3) (2014), pp. 277–300.
  • L. Barreira and C. Valls, On two notions of exponential dichotomy, Dyn. Syst. 33(4) (2018), pp. 708–721.
  • E. Bekryaeva, On the uniformness of estimates for the norms of solutions of exponentially dichotomous systems, Differ. Uravn. 46(5) (2010), pp. 626–636.
  • A. Czornik, K. Kitzing, and S. Siegmund, Spectra based on Bohl exponents and Bohl dichotomy for nonautonomous difference equations, J. Dynam. Differ. Equ. (2023). https://doi.org/10.1007/s10884-023-10311-0.
  • T.S. Doan, K.J. Palmer, and M. Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, J. Dynam. Differ. Equ. 29(4) (2017), pp. 1459–1485.
  • S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, New York, 2005.
  • N.A. Izobov, Lyapunov Exponents and Stability, Cambridge Scientific Publishers, Cambridge, 2012.
  • V.M. Millionščikov, Instability of the characteristic exponents of statistically regular systems, Mat. Zametki 2 (1967), pp. 315–318.

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.