On Regularity, Transitivity, and Ergodic Principle for Quadratic Stochastic Volterra Operators

Robust transitivity implies almost robust ergodicity

In this paper we show the relation between robust transitivity and robust ergodicity for conservative diffeomorphisms. In dimension 2 robustly transitive systems are robustly ergodic. For the three dimensional case, we define it almost robust ergodicity and prove that generically robustly transitive systems are almost robustly ergodic, if the Lyapunov exponents are nonzero. We also show in higher dimensions, that under some conditions robust transitivity implies robust ergodicity.

Ergodic Volterra Quadratic Transformations of Symplex

In the paper a Volterra quadratic stochastic operators of three dimensional simplex into itself is considered.The full description of ergodic properties such operators is given.

Approximate transitivity of the ergodic action of the group of finite permutations of $\mathbb{N}$ on $\{0, 1 \}^{\mathbb{N}}$

In this paper we show that the natural action of the symmetric group acting on the product space $\{0, 1 \}^{\mathbb{N}} $ endowed with a symmetric measure is approximately transitive. We also extend the result to a larger class of probability measures.

Ergodicity for Stochastic Neutral Retarded Partial Differential Equations Driven by $α$-regular Volterra process

In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $α$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential equations and the stochastic evolution equation, we get the ergodicity of neutral retarded stochastic functional differential equations.

Nearly approximate transitivity (AT) for circulant matrices

By previous work of Giordano and the author, ergodic actions of $\Z$ (and other discrete groups) are completely classified measure-theoretically by their dimension space, a construction analogous to the dimension group used in C*-algebras and topological dynamics. Here we investigate how far from AT (approximately transitive) can actions be which derive from circulant (and related) matrices. It turns out not very: although non-AT actions can arise from this method of construction, under very modest additional conditions, ATness arises; in addition, if we drop the positivity requirement in the …

与置换对应的一族非Volterra二次算子

A family of non-Volterra quadratic operators corresponding to permutations

本文研究一族参数化的非Volterra二次随机算子，确定其所有不动点，构造Lyapunov函数，完整描述极限点集并证明遍历性。