KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 5

Chaotic behaviour of maps possessing the almost average shadowing property

Mukta Garg
Ruchi Das
Sayfa
1371–1383
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Our study is supported by providing counter-examples wherever necessary.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we investigate the chaotic behaviour of maps having the almost average shadowing property by obtaining the relationship of the almost average shadowing property with different kinds of chaos.
📊
Temel Bulgular & Veri:Moreover, we relate the notion of almost average shadowing property with some other types of shadowing properties, for instance, ergodic shadowing, $\mathcal{F}_{\underline{d}}$-shadowing and $\underline{d}$-shadowing.
💡
Sonuç & Katkı:Our study is supported by providing counter-examples wherever necessary.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:almost average shadowing property · topological entropy · chaos

Abstract

In this paper, we investigate the chaotic behaviour of maps having the almost average shadowing property by obtaining the relationship of the almost average shadowing property with different kinds of chaos. Moreover, we relate the notion of almost average shadowing property with some other types of shadowing properties, for instance, ergodic shadowing, $\mathcal{F}_{\underline{d}}$-shadowing and $\underline{d}$-shadowing. We also study the notion of almost average shadowing property for maps induced on hyperspaces. Our study is supported by providing counter-examples wherever necessary.

🔖

Bu Makaleye Atıf Yap

Garg, M., Das, R. (2022). Chaotic behaviour of maps possessing the almost average shadowing property. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 5, 1371–1383. https://ajindex.com/articles/529452

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (20)

  1. E. Akin and S. Kolyada, Li-Yorke sensitivity, Nonlinearity, 16, 1421–1433, 2003
  2. T. Arai and N. Chinen, P-chaos implies distributional chaos and chaos in the sense of Devaney with positive topological entropy, Topology Appl. 154, 1254–1262, 2007
  3. W. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures, Monatsh. Math. 79, 81–92, 1975
  4. F. Blanchard, E. Glasner, S. Kolyada and A. Maass, On Li-Yorke pairs, J. Reine Angew. Math. 547, 51–68, 2002
  5. M.L. Blank, Metric properties of ϵ-trajectories of dynamical systems with stochastic behaviour, Ergodic Theory Dynam. Systems, 8, 365–378, 1988
  6. R. Das and M. Garg, Average chain transitivity and the almost average shadowing property, Commun. Korean Math. Soc. 32, 201–214, 2017
  7. D.A. Dastjerdi and M. Hosseini, Sub-shadowings, Nonlinear Anal. 72, 3759–3766, 2010
  8. Y. Dong, X. Tian and X. Yuan, Ergodic properties of systems with asymptotic average shadowing property, J. Math. Anal. Appl. 432, 53–73, 2015
  9. A. Fakhari and F.H. Ghane, On shadowing: ordinary and ergodic, J. Math. Anal. Appl. 364, 151–155, 2010
  10. M. Garg and R. Das, Relations of the almost average shadowing property with ergod- icity and proximality, Chaos Solitons Fractals, 91, 430–433, 2016
  11. R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal. 67, 1680–1689, 2007
  12. R. Gu and W. Guo, On mixing property in set-valued discrete systems, Chaos Solitons Fractals 28, 747–754, 2006
  13. J.L.G. Guirao, D. Kwietniak, M. Lampart, P. Oprocha and A. Peris, Chaos on hy- perspaces, Nonlinear Anal. 71, 1–8, 2009
  14. W. Huang and X. Ye, Devaney’s chaos or 2-scattering implies Li-Yorke’s chaos, Topology Appl. 117, 259–272, 2002
  15. M. Kulczycki, A unified approach to theories of shadowing, Regul. Chaotic Dyn. 19, 310–317, 2014
  16. M. Kulczycki, D. Kwietniak and P. Oprocha, On almost specification and average shadowing properties, Fund. Math. 224, 241–278, 2014
  17. M. Kulczycki and P. Oprocha, Properties of dynamical systems with the asymptotic average shadowing property, Fund. Math. 212, 35–52, 2011
  18. K. Lee and K. Sakai, Various shadowing properties and their equivalence, Discrete Contin. Dyn. Syst. 13, 533–540, 2005
  19. R. Li, A note on chaos via Furstenberg family couple, Nonlinear Anal. 72, 2290–2299, 2010
  20. R. Li, A note on shadowing with chain transitivity, Commun. Nonlinear Sci. Numer. Simul. 17, 2815–2823, 2012