真拟弱几乎周期点和拟正则点

T为紧致度量空间X上的连续映射,M（X）为X上所有Borel概率测度.设x∈X,记Mx（T）为概率测度序列{1n∑n 1i=0δTi（x）}在M（X）中的极限点的集合,其中δx表示支撑集是{x}的点测度.记W（T）和QW（T）分别为T的弱几乎周期点和拟弱几乎周期点集.本文证明,如果（X,T）非平凡且满足specifcation性质,则存在x,y∈QW（T）／W（T）（称为真拟弱几乎周期点）,分别满足μ∈Mx（T）,x∈Supp（μ）和ν∈My（T）,y∈/Supp（ν）,回答了周作领等提出的公开问题.Mx（T）在弱拓扑中是紧致连通集,所以,要么是单点集,要么是不可数集.如果x∈QW（T）／W（T）,则Mx（T）是不可数集.一个自然的问题是,怎么刻画M x（T）是单点集的点x（这时x称为拟正则点）.本文给出M x（T）是单点集的充要条件.     

CONSTRUCTIONS OF THE INVARIANT SETS AND INVARIANT MEASURES

In this paper, we will discuss the constructiOn problems about the invariant sets and invariant measures of continues maps~ which map complexes into themselves, using simplical approximation and Markov cbeirs. In [7], the author defined a matrix by using r-normal subdivi of the w,dimensional unit cube, considered it a Markov matrix, and constructed the invariantset and invafiant measure, In fact, the matrix he defined is not Markov matrix generally. So wewill give [7] and amendment in the last pert of this paper. We also construct an invariant set thatis the chain-recurrent set of the map by means of a non-negative matrix which only depends on themap. At hst, we will prove the higher dimension?Banach variation formuls that can simplify thetransition matrix.     

Stochastic Cahn-Hilliard equations driven by Poisson random measures

We study a stochastic Cahn-Hilliard equation driven by a Poisson random measure with Neumann boundary conditions. The global weak solution is established for the equation. Moreover, the existence of a Lyapunov function for the equation and an invariant measure associated with the transition semigroup are proved.     

流上一类强敏感依赖性的注记

证明敏感依赖的且有满测度中心的连续流是遍历敏感依赖的;连续流是遍历敏感依赖的当且仅当其乘积是遍历敏感依赖的.     

On Vitali's Theorem for Groups of Motions of Euclidean Space

We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [1] holds true. This characterization is formulated in purely geometrical terms.     

The triangular maps with closed sets of periodic points

In a recent paper we provided a characterization of triangular maps of the square, i.e., maps given by F(x,y)=(f(x),gx(y)), satisfying condition (P1) that any chain recurrent point is periodic. For continuous maps of the interval, there is a list of 18 other conditions equivalent to (P1), including (P2) that there is no infinite ω-limit set, (P3) that the set of periodic points is closed and (P4) that any regularly recurrent point is periodic, for instance. We provide an almost complete classification among these conditions for triangular maps, improve a result given by C. Arteaga [C. Arteaga, Smooth triangular maps of the square with closed set of periodic points, J. Math. Anal. Appl. 196 (1995) 987-997] and state an open problem concerning minimal sets of the triangular maps. The paper solves partially a problem formulated by A.N. Sharkovsky in the eighties. The mentioned open problem, the validity of (P4) ⇒ (P3), is related to the question whether some regularly recurrent point lies in the fibres over an f-minimal set possessing a regularly recurrent point. We answered this question in the positive for triangular maps with nondecreasing fiber maps. Consequently, the classification is completed for monotone triangular maps.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

The structure on invariant measures of <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> generic diffeomorphisms

Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ.     

Contributions to a Rigidity Conjecture

Let p and q be two relatively prime positive integers and a Borel probability measure invariant and ergodic by the semigroup generated by the action of both zp and zq. We analyse sufficient conditions to guarantee that is either the Lebesgue measure or supported on a periodic orbit. And extend the results for general expanding differentiable maps of the circle.     

Periodic number for Anosov maps

LetX be a compact metric space and letf: X→X be an Anosov map,i.e., an expansive selfmap with the pseudoorbit tracing property (abbr. POTP) (see Lemma 1). IfNn(f) denotes the number of fixed points off ⁿ which we name here then-periodic number then we prove in the case asn tends to infinity thatn ^M ≤N_n(f)≤Hⁿ, whereM andH are two positive integers.     

Random Logistic Maps. I

Let {C _i} ₀ be a sequence of independent and identically distributed random variables with vales in [0, 4]. Let {X _n} ₀ be a sequence of random variables with values in [0, 1] defined recursively by X _n+1=C _n+1 X _n(1–X _n). It is shown here that: (i) E ln C ₁<0X _n0 w.p.1. (ii) E ln C ₁=0X _n0 in probability (iii) E ln C ₁>0, E |ln(4–C ₁)| such that (0, 1)=1 and is invariant for {X _n}. (iv) If there exits an invariant probability measure such that {0}=0, then E ln C ₁>0 and – ln(1–x) (dx)=E ln C ₁. (v) E ln C ₁>0, E |ln(4–C ₁)|< and {X _n} is Harris irreducible implies that the probability distribution of X _n converges in the Cesaro sense to a unique probability distribution on (0, 1) for all X ₀0.     

Some remarks on spherically invariant distributions

We consider the notion of a spherically invariant measure on a real and separable Hilbert space and study some equivalence properties of measures of this type. The latter are of interest in statistical communication theory.     

抽象对偶对上的滑脊性(英文)

给出F-弱滑脊性的定义,利用此性质,证明如果λ是一个具有F-弱滑脊性的数量空间,λ-乘数无序收敛是一个对偶不变性.如果(λ,β(λ,λ~(uβ)))是FAK-空间,则上述性质变成全程不变性.