Ergodicities of Infinite Dimensional Nonlinear Stochastic Operators

• Mukhamedov Farrukh ^[1] ; Khakimov Otabek ^[3] ; Embong, Ahmad Fadillah ^[2]
  1. [1] United Arab Emirates University

     United Arab Emirates University

     Emiratos Árabes Unidos

     
  2. [2] University of Technology Malaysia

     University of Technology Malaysia

     Malasia

     
  3. [3] Institute of Mathematics (Tashkent, Uzbekistan)

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
• Idioma: inglés
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• Resumen

  • In the present paper, we introduce two classes L+ and L- of nonlinear stochastic operators acting on the simplex of ℓ1-space. For each operator V from these classes, we study omega limiting sets ωV and ωV(w) with respect to ℓ1-norm and pointwise convergence, respectively. As a consequence of the investigation, we establish that every operator from the introduced classes is weak ergodic. However, if V belongs to L-, then it is not ergodic (w.r.t ℓ1-norm) while V is weak ergodic.