Araştırma Makalesi
Yıl 2021,
, 483 - 491, 11.04.2021
Öz
In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators. We prove that for a linear IFS, hypercyclicity implies sensitivity and if an IFS is abelian, then hypercyclicity also implies multi-sensitivity and hence thick sensitivity. We also give some equivalent conditions for hypercyclicity as well as weakly mixing for an IFS of operators.
Anahtar Kelimeler
Iterated function systems hypercyclic operators sensitive operators weakly mixing operators
Kaynakça
- [1] A.Z. Bahabadi, Shadowing and average shadowing properties for iterated function systems, Georgian Math. J. 22, 179–184, 2015.
- [2] A.Z. Bahabadi, On chaos for iterated function systems, Asian-Eur. J. Math. 11, 1850054, 2018.
- [3] F. Bayart and É. Matheron, Dynamics of linear operators, 179, Cambridge University Press, Cambridge, 2009.
- [4] G. Costakis and A. Manoussos, J-class operators and hypercyclicity, J. Operator Theory, 67, 101–119, 2012.
- [5] J.H. Elton and M. Piccioni, Iterated function systems arising from recursive estima- tion problems, Probab. Theory Related Fields, 91, 103–114, 1992.
- [6] B. Forte and E.R. Vrscay, Solving the inverse problem for function/image approxi- mation using iterated function systems. II. Algorithm and computations, Fractals, 2, 335–346, 1994.
- [7] F.H. Ghane, E. Rezaali, and A. Sarizadeh, Sensitivity of iterated function systems, J. Math. Anal. Appl. 469, 493–503, 2019.
- [8] K-G. Grosse-Erdmann and A. Peris, Weakly mixing operators on topological vector spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 104, 413–426, 2010.
- [9] K-G. Grosse-Erdmann and A. Peris, Linear chaos, Springer Science & Business Media, 2011.
- [10] J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30, 713–747, 1981.
- [11] M. Kostić, Chaos for linear operators and abstract differential equations, Nova Science Publishers, New York, 2020.
- [12] C. Ma and P. Zhu, A remark on sensitivity and Li-Yorke sensitivity of iterated func- tion systems, Qual. Theory Dyn. Syst. 18, 1–9, 2019.
- [13] M. Mohtashamipour and A.Z. Bahabadi, Accessibility on iterated function systems, Georgian Math. J. 28 (1), 117–124, 2021.
- [14] T.K.S. Moothathu, Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20, 2115–2126, 2007.
- [15] M. Murillo-Arcila and A. Peris, Chaotic behaviour on invariant sets of linear opera- tors, Integral Equations Operator Theory, 81, 483–497, 2015.
- [16] M. Salman and R. Das, Furstenberg family and multi-sensitivity in non-autonomous systems, J. Difference Equ. Appl. 25, 1755–1767, 2019.
- [17] M. Salman and R. Das, Multi-transitivity in non-autonomous discrete systems, Topol- ogy Appl. 278, 107237, 2020.
- [18] M. Salman and R. Das, Sensitivity and property $P$ in non-autonomous systems, Mediterr. J. Math. 17, 128, 2020.
- [19] X.Wu, S. Liang, Y. Luo, M. Xin and X. Zhang, A remark on limit shadowing property for iterated function systems, U.P.B. Sci. Bull. Series A, Appl. Math. Phys. 81, 107– 114, 2019.
- [20] X. Wu, L. Wang and J. Liang, The chain properties and average shadowing property of iterated function systems, Qual. Theory Dyn. Syst. 17, 219–227, 2018.
- [21] X. Wu and P. Zhu, On the equivalence of four chaotic operators, Appl. Math. Lett. 25, 545–549, 2012.
- [22] X. Zhang, X. Wu, Y. Luo and X. Ma, A remark on limit shadowing for hyperbolic iterated function systems, U.P.B. Sci. Bull., Series A, Appl. Math. Phys. 81, 139–146, 2019.
Yıl 2021,
, 483 - 491, 11.04.2021
Öz
Kaynakça
- [1] A.Z. Bahabadi, Shadowing and average shadowing properties for iterated function systems, Georgian Math. J. 22, 179–184, 2015.
- [2] A.Z. Bahabadi, On chaos for iterated function systems, Asian-Eur. J. Math. 11, 1850054, 2018.
- [3] F. Bayart and É. Matheron, Dynamics of linear operators, 179, Cambridge University Press, Cambridge, 2009.
- [4] G. Costakis and A. Manoussos, J-class operators and hypercyclicity, J. Operator Theory, 67, 101–119, 2012.
- [5] J.H. Elton and M. Piccioni, Iterated function systems arising from recursive estima- tion problems, Probab. Theory Related Fields, 91, 103–114, 1992.
- [6] B. Forte and E.R. Vrscay, Solving the inverse problem for function/image approxi- mation using iterated function systems. II. Algorithm and computations, Fractals, 2, 335–346, 1994.
- [7] F.H. Ghane, E. Rezaali, and A. Sarizadeh, Sensitivity of iterated function systems, J. Math. Anal. Appl. 469, 493–503, 2019.
- [8] K-G. Grosse-Erdmann and A. Peris, Weakly mixing operators on topological vector spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 104, 413–426, 2010.
- [9] K-G. Grosse-Erdmann and A. Peris, Linear chaos, Springer Science & Business Media, 2011.
- [10] J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30, 713–747, 1981.
- [11] M. Kostić, Chaos for linear operators and abstract differential equations, Nova Science Publishers, New York, 2020.
- [12] C. Ma and P. Zhu, A remark on sensitivity and Li-Yorke sensitivity of iterated func- tion systems, Qual. Theory Dyn. Syst. 18, 1–9, 2019.
- [13] M. Mohtashamipour and A.Z. Bahabadi, Accessibility on iterated function systems, Georgian Math. J. 28 (1), 117–124, 2021.
- [14] T.K.S. Moothathu, Stronger forms of sensitivity for dynamical systems, Nonlinearity, 20, 2115–2126, 2007.
- [15] M. Murillo-Arcila and A. Peris, Chaotic behaviour on invariant sets of linear opera- tors, Integral Equations Operator Theory, 81, 483–497, 2015.
- [16] M. Salman and R. Das, Furstenberg family and multi-sensitivity in non-autonomous systems, J. Difference Equ. Appl. 25, 1755–1767, 2019.
- [17] M. Salman and R. Das, Multi-transitivity in non-autonomous discrete systems, Topol- ogy Appl. 278, 107237, 2020.
- [18] M. Salman and R. Das, Sensitivity and property $P$ in non-autonomous systems, Mediterr. J. Math. 17, 128, 2020.
- [19] X.Wu, S. Liang, Y. Luo, M. Xin and X. Zhang, A remark on limit shadowing property for iterated function systems, U.P.B. Sci. Bull. Series A, Appl. Math. Phys. 81, 107– 114, 2019.
- [20] X. Wu, L. Wang and J. Liang, The chain properties and average shadowing property of iterated function systems, Qual. Theory Dyn. Syst. 17, 219–227, 2018.
- [21] X. Wu and P. Zhu, On the equivalence of four chaotic operators, Appl. Math. Lett. 25, 545–549, 2012.
- [22] X. Zhang, X. Wu, Y. Luo and X. Ma, A remark on limit shadowing for hyperbolic iterated function systems, U.P.B. Sci. Bull., Series A, Appl. Math. Phys. 81, 139–146, 2019.
Toplam 22 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 11 Nisan 2021 |
| Yayımlandığı Sayı | Yıl 2021 |