Topological conditions for the existence of absorbing Cantor sets

This paper deals with strange attractors of S-unimodal maps . It generalizes earlier results in the sense that very general topological conditions are given that either

i)

guarantee the existence of an absorbing Cantor set provided the critical point of is sufficiently degenerate, or

ii)

prohibit the existence of an absorbing Cantor set altogether.

As a by-product we obtain very weak topological conditions that imply the existence of an absolutely continuous invariant probability measure for .

     

Strong Consistency of the Maximum Product of Spacings Estimates with Applications in Nonparametrics and in Estimation of Unimodal Densities

Distributions with unimodal densities are among the most commonly used in practice. However, for many unimodal distribution families the likelihood functions may be unbounded, thereby leading to inconsistent estimates. The maximum product of spacings (MPS) method, introduced by Cheng and Amin and independently by Ranneby, has been known to give consistent and asymptotically normal estimators in many parametric situations where the maximum likelihood method fails. In this paper, strong consistency theorems for the MPS method are obtained under general conditions which are comparable to the conditions of Bahadur and Wang for the maximum likelihood method. The consistency theorems obtained here apply to both parametric models and some nonparametric models. In particular, in any unimodal distribution family the asymptotic MPS estimator of the underlying unimodal density is shown to be universally L¹ consistent without any further conditions (in parametric or nonparametric settings).     

幂等自映照的Nielsen数

设X是一个有限且连通的多面体,f是x上的一个好幂等自映照,则f的Nielsen数不超过1.     

Decay of correlations for Fibonacci unimodal interval maps

We consider a class of generalized Fibonacci unimodal maps for which the central return times {s_n} satisfy that s_n = s_(n-1) +ks_(n-2) for some k ≥ 1. We show that such a unimodal map admits a unique absolutely continuous invariant probability with exactly stretched exponential decay of correlations if its critical order lies in(1, k+1).     

Potential kernels,probabilities of hitting a ball,harmonic functions and the boundary Harnack inequality for unimodal Lévy processes

In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unimodal Lévy processes. We also prove a supremum estimate and a regularity result for functions harmonic with respect to a general isotropic unimodal Lévy process.In the second part we apply the recent results on the boundary Harnack inequality and Martin representation of harmonic functions for the class of isotropic unimodal Lévy processes. As a sample application, we provide sharp two-sided estimates of the Green function of a half-space.     

完备稠序线性序拓扑空间上的奇周期轨序关系

研究完备稠序线性序拓扑空间上连续自映射的周期轨,指出当连续自映射有（2n＋1）-周期轨而没有（2n-1）-周期轨时,该（2n＋1）-周期轨上各点的序关系.利用这个关系将Sharkovskii定理从实直线推广到完备稠序线性序拓扑空间上。     

马尔可夫随机过程中移动对象的空间特征分析及近似逼近研究

研究一类移动对象在马尔可夫（马氏）随机过程中的空间逼近问题.首先运用数学推理方式获得时空网络马尔可夫随机模型的一种状态转移函数.定义时空网络为移动对象及其移动轨迹形成的三维空间,建立马尔可夫随机过程的距离空间,证明了相应环境下的不动点理论.通过分析和扩展状态转移函数得到距离空间的自映射算子,从原节点映射到目标节点,达到对象的移动,并对此进行了理论证明和仿真实验验证.在此基础上从应用层面出发,尝试性地进行了移动对象的空间粒度分解,利用不动点映射更好地定位移动对象,实时满足移动对象的需求.相关实验进一步验证了空间分析的可行性和有效性. 关键词： 马尔可夫随机过程 距离空间 不动点 自映射算子     

Unimodal mappings and Li-Yorke chaos

Conditions for unimodal mappings to have domains with a Li-Yorke chaotic behavior of trajectories are found. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 679–689, May, 1998.     

单峰函数族符号序列与对应参数大小一致的一个充分条件

运用符号动力学方法研究单峰函数族λf(x)符号序列与其对应参数的相互关系, 给出单峰函数族符号序列与对应参数大小一致的一个充分条件.     

Controlling the Cournot-Nash Chaos

The recently developing theory of nonlinear dynamics shows that any economic model can generate a complex dynamics involving chaos if the nonlinearities become strong enough. This study constructs a nonlinear Cournot duopoly model, reveals conditions for the occurrence of chaos, and then considers how to control chaos. The main purpose of this paper is to demonstrate that chaos generated in Cournot competition is in a double bind from the long-run perspective: a firm with a lower marginal production cost prefers a stable (i.e., controlled) market to a chaotic (i.e., uncontrolled) market, while a firm with a higher marginal cost prefers the chaotic market. Helpful remarks and comments by Ferenc Szidarovszky, Michael Kopel, Shahriai Yousefi, and three anonymous referees are gratefully acknowledged. Financial support from the Japan Ministry of Education, Culture, Sports, Science, and Technology, Grant-in-Aid for Scientific Research (B)15330037, and from Chuo University, Joint Research Grant 0382, is highly appreciated.