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我们系统可以在很大的能量范围内都是遍历状态的方案。In a large range of energy the system is ergodic.

本文研究拓扑遍历映射。This paper deals with topologically ergodic maps.

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弱遍历是在紧致系统上的一种新的遍历概念。Weakly ergodic is a new ergodic conception on compact system.

第三章，考虑离散群的混沌作用。In chapter 4, we consider the ergodic properties of group actions.

在遍历性的假设条件下讨论了一类积分方程遍历性解的存在性。The authors discuss the existence of ergodic solutions of some integ.

在遍历函数的基础上，引入了遍历序列的概念。Based on the ergodic functions, we first introduce the definition of ergodic sequence.

提出了一种基于遍历矩阵和DWT的图像鲁棒水印新算法。A novel robust image watermarking algorithm based on ergodic matrix and DWT is proposed.

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作为遍历理论的应用，讨论一类极限的求法。As an application of the ergodic theory, we discuss the method of calculating a type of limits.

接收信噪比较大时，平均信道容量上下限基本接近其实际值。And at high SNR, the upper and lower bounds on the ergodic capacity are close to its true value.

遍历定理和不变测度的存在性是遍历理论中的二个基本研究主题。Ergodic theorems and the existence of invariant measures are two major topics in Ergodic theory.

提出一种分析配电网供电可靠性的遍历递归算法。An ergodic recursive Algorithm is suggested for the analyse of the reliability of distribution grid.

在第五章里，我们得到了常返右过程的不变测度的存在性、唯一性及其遍历性。In chapter 5, we obtain the invariant measure and the ergodic property of recurrent right processes.

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在遍历性的假设条件下讨论了一类积分方程遍历性解的存在性。The authors discuss the existence of ergodic solutions of some integral equations under the assumption of ergodicity.

本文作为平稳集值随机过程的表示定理的应用，证明了平稳集值随机过程的遍历性定理。In this paper, we prove the ergodic theorem of a stationary set valued stochastic process by the representation theorem.

在第三章，对于硬球系统，只要球的个数N大于1，系统就是遍历和混合的。It is found that for the hard-ball systems, as long as the number of balls N exceeds 1, the system is ergodic and mixing.

用混沌态矢的特征解释了原子核的各态历经集体态的衰变特性。The decay behavior of the nuclear ergodic collective states is explained in terms of the peculiar property of chaotic states.

第三章研究一类非齐次马氏链的收敛速度及绝对平均强遍历性。In the third chapter, we study the rate of convergence of nonhomogeneous Markov chains and the absolute average strong ergodic.

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我们也证明了K-正则预解算子族的遍历极限的收敛率和逼近的一些结果。Finally, we obtain some results of the convergence rates of ergodic limits and approximation for K-regularized resolvent families.

理论分析和仿真结果表明，IAF方式在遍历容量和误码差错性能上均优于传统AF方式。Theoretical analysis and simulation results show that the IAF outperforms the AF method both in ergodic capacity and SER performance.

不均匀热电势沿铜铁合金热电极长度上的分布可描述为各态历经的平稳的随机过程。The distribution of inhomogeneous thermo-emf along the copper-iron thermoelectrode is described as a stationary ergodic random process.