On Non-ergodic Volterra Cubic Stochastic Operators

Farrukh Mukhamedov, Chin Hee Pah, Azizi Rosli

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Let Sm - 1 be the simplex in Rm, and V: Sm - 1→ Sm - 1 be a nonlinear mapping then this operator satisfies an ergodic theorem if the limit limn→∞1n∑k=1nVk(x)exists for every x∈ Sm - 1. It is a well known fact that this ergodicity may fail for Volterra quadratic operators, so it is natural to characterize all non-ergodic operators. However, there is an ongoing problem even in the low dimensional simplexes. In this paper, we solve the mentioned problem within Volterra cubic stochastic operators acting on two-dimensional simplex.

Original languageEnglish
Pages (from-to)1225-1235
Number of pages11
JournalQualitative Theory of Dynamical Systems
Issue number3
Publication statusPublished - Dec 1 2019


  • Cubic stochastic operator
  • Dynamics
  • Non-ergodic
  • Volterra operator

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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