解对初值连续依赖定理的一个新的证明方法

《常微分方程》传统的教材均先证明Bellman引理,然后利用Bellman引理完成"解对初值连续依赖定理"的证明.本文用曲线平移的方法构造出比较函数,从而给出了解对初值连续依赖定理的一种新的且具有几何直观性的证明方法.     

On Lyapunov exponent and sensitivity

Sensitive dependence on initial conditions is widely understood as being the central idea of chaos. For a large class of transformations of the interval, we prove that positiveness of the Lyapunov exponent implies the sensitivity property. We also provide bounds for the sensitivity constant.     

The central limit theorem and chaos

Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.     

Integro-Local and Integral Limit Theorems on the Large Deviations of Sums of Random Vectors: Regular Distributions

We study the asymptotics of the probability that the sum of random vectors belongs to a relatively small cube in the range of large deviations.     

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In this paper, we first study the strong law of large numbers for the frequencies of occurrence of random ordered couples of states for nonhomogeneous bifurcating Markov chains indexed by a binary tree. Then the strong law of large numbers are studied for functions of the nonhomogeneous bifurcating Markov chains indexed by a binary tree. As a corollary, we obtain the shannon-McMillan theorem for these Markov chains with finite state space.