On Dynamics of ℓ- Volterra Quadratic Stochastic Operators

2007/12/24 by U. A. Rozikov, Rozikov, U. A., Akbar Zada +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #37XX #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0712.3979

openalex publication_date 2007/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of ℓ-Volterra quadratic stochastic operator defined on (m-1)-dimensional simplex, where ℓ∈\0,1,...,m\. The ℓ-Volterra operator is a Volterra operator iff ℓ=m. We study structure of the set of all ℓ-Volterra operators and describe their several fixed and periodic points. For m=2 and 3 we describe behavior of trajectories of (m-1)-Volterra operators. The paper also contains many remarks with comparisons of ℓ-Volterra operators and Volterra ones.

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