Orbits of random dynamical systems

Ahmed Zaou; Otmane Benchiheb; Mohamed  Amouch

doi:10.5269/bspm.64370

Ahmed Zaou University Chouaib Doukkali
Otmane Benchiheb Université Chouaïb Doukkali https://orcid.org/0000-0002-6759-2368
Mohamed Amouch University Chouaib Doukkali https://orcid.org/0000-0002-4613-0068

Résumé

In this paper we introduce and study the notions of hypercyclicity and transitivity for random dynamical systems
and we establish the relation between them in a topological space. We also introduce the notions of mixing and
weakly mixing for random dynamical systems and give some of their properties.

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Références

M. Amouch, O. Benchiheb, On cyclic sets of operators, Rendiconti del Circolo Matematico di Palermo Series 2, 68, 521-529, 2019.

M. Amouch, and O. Benchiheb. ”On linear dynamics of sets of operators.” Turkish Journal of Mathematics 43.1 (2019): 402-411.

M. Amouch, O. Benchiheb, Diskcyclicity of sets of operators and applications, Acta Mathematica Sinica, English Series. 36, 1203-1220, 2020.

M. Amouch, O. Benchiheb, Some versions of supercyclicity for a set of operators, Filomat, 35, 1619-1627, 2021.

M. Amouch, O. Benchiheb. Codiskcyclic sets of operators on complex topological vector spaces, Proyecciones Journal (2022).

M. Amouch, O. Benchiheb. On recurrent sets of operators. arXiv:1907.05930v3 [math.FA] 7 May 2022

M. Ansari, B. Khani-Robati, K. Hedayatian. On the density and transitivity of sets of operators. Turkish Journal of Mathematics 42.1, 181-189, 2018.

M. Ansari, K. Hedayatian, B. Khani-Robati, A. Moradi. A note on topological and strict transitivity. Iranian Journal of Science and Technology, Transactions A: Science, 42(1), 59-64, 2018.

F. Bayart, E Matheron. Dynamics of linear operators. 2009; New York, NY, USA, Cambridge University Press, 2009.

J. P. Bes. Three problem’s on hypercyclic operators. Ph.D. thesis, Bowling Green State University, Bowling Green, Ohio, 1998.

J. P. Bes, A. Peris. Hereditarily hypercyclic operators. Journal of Functional Analysis 167.1, 94-112, 1999.

G. D. Birkhoff. Surface transformations and their dynamical applications. Acta Mathematica, 43, 1-119, 1922.

M. De La Rosa, C. Read. A hypercyclic operator whose direct sum T⊕T is not hypercyclic. Journal of Operator Theory 369-380, 2009.

C. Kitai. Invariant closed sets for linear operators. 1148-1148, (984.

M. Kostic. Chaos for linear operators and abstract differential equations. Nova Science Publishers, 2020.

R. M. Gethner, J. H. Shapiro. Universal vectors for operators on spaces of holomorphic functions. Proceedings of the American Mathematical Society 100.2, 281-288, 1987.

K-G. Grosse-Erdmann, A. Peris Manguillot. Linear chaos. Springer Science and Business Media, 2011.

K-G. Grosse-Erdmann. Universal families and hypercyclic operators. Bulletin of the American Mathematical Society 36.3, 345-381, 1999.

A. Ludwig. Trends and open problems in the theory of random dynamical systems. Probability towards 2000. Springer, New York, NY, 34-46, 1998.

S. Rolewicz. On orbits of elements. Studia Mathematica, 32.1, 17-22, 1969.