共查询到18条相似文献,搜索用时 93 毫秒
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介绍了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续的概念,利用乘积映射的性质,研究了乘积映射f×g与分映射f和g在这些动力学性质方面的关系,得到如下结果:1)乘积映射f×g具有G-周期跟踪性当且仅当f具有G_1-周期跟踪性,g具有G_2-周期跟踪性;2)乘积映射f×g具有G-等度连续当且仅当f具有G_1-等度连续,g具有G_2-等度连续.这些结论弥补了拓扑群作用下乘积空间中G-周期跟踪性和G-等度连续理论的缺失. 相似文献
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逐点伪轨跟踪性质及其应用 总被引:5,自引:1,他引:5
本文给出紧致度量空间逐点伪轨跟踪性质的定义,该定义是伪轨跟踪性质定义的推广.作为应用,证明如下结论:(i)若f具有逐点伪轨跟踪性质,且对任意k∈Z ,fk为链转换的,那么对任意k∈Z ,fk为开集转换;(ii)若f具有逐点伪轨跟踪性质,且对任意n∈Z ,fn为链转换的,则f具有初始敏感依赖性质;(iii)若f为开集混合的,且具有逐点伪轨跟踪性质,那么f具有性质P;(iv)设f:(X,d)→(X,d)是同胚映射,那么f具有逐点伪轨跟踪性质当且仅当移位映射σf具有逐点伪轨跟踪性质. 相似文献
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P0-函数箱约束变分不等式的正则半光滑牛顿法 总被引:8,自引:0,他引:8
1引言设X C R~n,F:R~n→R~n,变分不等式Ⅵ(X,F)是指:求x∈X,使F(x)~T(y-x)≥0,(?)_y∈X.(1)记i∈N={1,2,…,n},当X=[a,b]:={x∈(?)~n|a_i≤x_i≤b_i,i∈N}时,称Ⅵ(X,F)为箱约束变分不等式(也有些文献称为混合互补问题),记为Ⅵ(a,b,F).若a_i=0,b_i= ∞,i∈N,即X=(?)_ ~n:={x∈(?)~n|x≥0}时,Ⅵ(a,b,F)化为非线性互补问题NCP(F):求x∈(?)_ ~n,使x≥0,F(x)≥0,x~TF(x)=0.(2) 相似文献
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曾六川 《数学物理学报(A辑)》2004,24(3):299-306
设C是具有弱一致正规结构的Banach空间X的非空弱紧凸子集, T={T(t):t∈S}是渐近非扩张型半群, 且每个T(t)在C上连续. 该文证明了如下结论:(i) 若X是一致凸的, 则F(T) 非空;(ii) 若T={T(t):t∈S}满足lim inf_{t→∞,t in S}|‖T(t)‖|<+∞, 且在C上弱渐近正则, 则F(T)非空, 其中|‖T(t)‖|是T(t)的精确的Lipsch itz常数,F(T)是T(t),t∈S的所有公共不动点之集. 相似文献
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给出了Rn上的线性同构和线性流具有极限跟踪性的特征:线性同构具有极限跟踪性当且仅当其对应的矩阵为双曲的;线性流具有极限跟踪性当且仅当其对应矩阵的所有特征根均具有非零实部. 相似文献
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本文给出几乎可裂序列的Green对应.主要结果为:设X是不可分解非投射kG-模,Y是相应的不可分解非投射kL-模,那么(i)0→Ω~2(X)→(XU)_0→X→0是可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是可裂正和列;(ⅱ)0→Ω~2(X)→(X(U)_0→X→0是几乎可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是几乎可裂正和列. 相似文献
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d-和d-跟踪性质是Dastjerdi和Hosseini为推广伪轨跟踪性质于2010年提出的.本文考察该动力性质在迭代系统和逆极限系统下的性质.首先证明对动力系统(X,f),以下三命题等价:(1)f具有d-跟踪性质(d-跟踪性质);(2)对任意k∈N,f~k也具有d-跟踪性质(d-跟踪性质);(3)存在k∈N,使得f~k具有d-跟踪性质(d-跟踪性质).进而证明具有d-跟踪性质的系统是链混合的.最后得到对于由{X_i,φ_i,f_i)_(i=1)~∞生成的逆极限系统(X_∞,f_∞),若每个f_i均具有d-跟踪性质(或者,d-跟踪性质,遍历跟踪性),则诱导映射f_∞也具有d-跟踪性质(相应地,d-跟踪性质,遍历跟踪性). 相似文献
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设f为一个算术函数,S={x 1,…,x n}为一个n元正整数集合.称S为gcd-封闭的, 如果对于任意1 i,j n,均有(x i,x j)∈S.以 ={y 1,…,y m}表示包含S的最小gcd-封闭的正整数集合. 设(f(x i,x j))表示一个n×n矩阵, 其(i,j)项为f在x i与x j的最大公因子(x i,x j)处的值. 设(f[x i,x j])表示一个n×n矩阵, 其(i,j)项为f在x i与x j的最小公倍数[x i.xj]处的值. 本文证明了: (i) 如果f∈C s ={f:(f*μ)(d)>0, x∈S,d|x},这里f*μ表示f与μ的Dirichlet乘积,μ表示M bius函数,那么 并且(1)取等号当且仅当S=;(ii)如果f为乘法函数,并且 ∈Cs,那么 并且(2)取等号当且仅当S= .不等式(1)和(2)分别改进了Bourque与Ligh在1993年和1995年所得到的结果. 相似文献
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求解不可微箱约束变分不等式的下降算法 总被引:2,自引:1,他引:1
1 引 论 设X(?)Rn是非空闭集,F:Rn→Rn连续映射,变分不等式问题VI(X,F)是指:求x∈X,使 F(x)T(y-x)≥0, (?)y∈X,(1)记指标集N=(1,2,…,n},当 X=[a,b]≡{x∈Rn|a≤xi≤bi,i∈N},(2)其中a={a1,a2,…,an}T,b={b1,b2,…,bn}T∈Rn时,VI(X,F)化为箱约束变分不等式VI(a,b,F).若ai=0,bi=+∞,i∈N,即X=R+n≡{x∈Rn|x≥0}时,VI(a,b,F)化为非线性 相似文献
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Let (X, d) be a bounded metric space and f : X → X be a uniformly continuous surjection. For a given dynamical system (X, f) which may not be compact, we investigate the relation between the asymptotic average shadowing property(AASP), transitivity and mixing. If f has the AASP, then the following statements hold: (1) f n is chain transitive for every positive integer n; (2) If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; (3) If f is equicontinuous, then f is topologically weakly mixing; (4) If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given. 相似文献
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In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property. 相似文献
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Acta Mathematica Sinica, English Series - The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a... 相似文献
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Yu Jun ZHU Jin Lian ZHANG Lian Fa HE 《数学学报(英文版)》2006,22(5):1321-1328
In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also "uniform" with respect to C^1 perturbation. 相似文献