最大平均度量下的Bowen维数熵与测度下局部熵

熵是反映动力系统复杂性的一个非常重要的量.本文研究了平均意义下的动力系统的性质,对于最大平均度量,引入了Bowen维数熵以及测度下局部熵的概念.并研究了它们之间的关系,说明了在最大平均度量下,Bowen维数熵依然可以由测度下局部熵估计.     

测度的上局部熵和集合的类Bowen熵

设f为度量空间(x,d)上的连续映射,该文主要讨论了x的任意子集关于f的类Bowen熵可以通过(x,d)上测度的上局部熵估计.     

非自治动力系统Bowen估计熵的变分原理

推广了经典动力系统的Bowen拓扑熵,给出了非自治动力系统的Bowen估计熵的定义,讨论了非自治动力系统的Bowen估计熵和局部估计熵的关系,推广了自治动力系统Bowen拓扑熵的Billingsley型定理,研究了非自治动力系统的Bowen α-估计熵的Billingsley型定理.此外,给出了非自治动力系统Bowen...     

一类Smale空间上的C~*-代数自同构的熵

Ian Putnam利用Smale空间上的渐近等价关系定义了广群C~*-代数及其典则自同构.本文在零维Smale空间的情形下,计算此类C~*-自同构的逼近熵,证明了相应C~*-动力系统关于CNT熵和逼近熵的"变分原理"成立.由此推演出此类Smale空间上的Bowen测度诱导的C~*-代数上的态是此典则自同构的唯一平衡态.     

可数无限群作用子集的单纯Bowen拓扑熵 献给杨乐教授80华诞

本文研究紧度量空间上可数无限群作用给出的动力系统G■X.特别地,对于X的任何一个子集Z,定义这个群作用相对于子集Z的单纯(naive) Bowen拓扑熵h_(top)~(nv)(G, Z).进一步,本文研究这种熵的基本性质,并且对于非顺从的可数无限群,计算这种熵的取值范围.事实证明,这种单纯熵的取值真的很单纯,反映了动力系统复杂度的一种二分现象.     

部分双曲动力系统中不稳定局部熵的重分形分析

本文在部分双曲动力系统中定义了Borel概率测度的不稳定局部熵.为了刻画不稳定局部熵的重分形谱,引入不稳定(q,μ)-熵的概念,给出不稳定(q,μ)-熵的基本性质,并建立了不稳定局部熵重分形谱的Bowen不稳定熵与(q,μ)-熵之间的关系式.     

k维环面上坐标自映射下拓扑熵的一个下界

给出了ｋ维环面上坐标自映射下拓扑熵的一个下界，最后，还指出了ｋ维环面上渐近Ｒｅｉｄｅｍｅｉｓｔｅｒ数严格大于渐近Ｎｉｅｌｓｅｎ数的情形，并说明了文（３）（或文（４）中引理１为该文的一个特例。     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

低复杂度序列的维数

本文研究符号空间中由零拓扑熵序列组成的集合.通过构造适当的自相似集,证明了该集合的盒维数为1,而Hausdorff维数为0.     

不变测度的Hausdorff维数和熵的关系

得到了紧致度量空间上可扩同胚的不变测度的Hausdorff维数和熵的几个关系式 ,并找到了熵为零的一个充要条件 .     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.