共查询到20条相似文献,搜索用时 62 毫秒
1.
本文考虑闭区间上变差有界的连续映射f:I→I的局部变差增长γ(x,f)与局部拓扑熵h(x,f).将证明γ(x,f)≥h(x,f)对所有x∈I成立,并且局部变差增长映射γf(x)=γ(x,f)与局部拓扑熵映射sf(x)=h(x,f)都是上半连续的,得到一个变分原理:局部变差增长γ(x,f)与局部拓扑熵h(x,f)的上确界分别等于全局变差增长γ(f)=limn→∞1/nln Var(fn)与拓扑熵h(f).当映射f:I→I拓扑传递时,与Brin 和Katok对局部(测度)熵的讨论类似,我们证明,至多除一个不动点外,局部变差增长γ(x,f)与局部拓扑熵h(x,f)在开区间I°内恒为常值. 相似文献
2.
图映射的吸引中心与拓扑熵 总被引:2,自引:0,他引:2
设f是图G上的连续自映射,P(f),AГ(f),ω(f),Ω(f),sα(y,f)分别表示f的周期点集,单侧γ-极限点集,ω-极限集,非游荡集,相对于y的特殊α-极限点集.本文证明了:(1)x∈sα(y,f)(对某个y∈G)当且仅当x∈sα(x,f)(2)AГ(f)∪P(f)包含∪y∈Gsα(y,f)(3)AГ(f)∪P(f)=ω(Ω(f))=ω(ω(f))=ω(∪y∈Gsα(y,f))=ω(∪(AГ(f)∪P(f)).此外,本文还得到了,具有正拓扑熵的几个等价条件。 相似文献
3.
一种点熵的估计与计算 总被引:2,自引:0,他引:2
对紧度量空间X上的连续自映射f:X→X,Hurley利用一点逆像的(n,ε),分离子集,引入了熵hp(f)和hm(f)。按照拓扑熵观点,它们也度量了系统(X,f)的复杂性,本文将以Nielsen根类理论为工具,首先给出hp(f)的一个恰当的下界估计;然后作为该结果的应用,我们具体计算了环面上一类自映射的熵hp(f),同时得到了该空间上自映射同伦类熵的一个下界估计。 相似文献
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设X是一个紧致度量空间,f:X→X是一个连续映射,(X,f)是熵极小的.该文首先证明了f是强遍历的;另外,如果还假设X中存在f的一个真的(拟)弱几乎周期点,则得到f具有正拓扑熵且对任意的n1,f~n是遍历敏感依赖的.因此,f在Li-Yorke和Takens-Ruelle意义下是混沌的.该文所得结论改进和推广了最近的一些结论. 相似文献
6.
对献[1]中圆周上扩张映射的拓扑熵的结论给予了改进,得到了结论:设f∈C^r(S^1,S^1)是扩张映射,则ent(f)=log│deg(f)│。 相似文献
7.
孙太祥 《高校应用数学学报(英文版)》2002,17(3):313-318
Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) fhas zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f^5 has a division; (2) If f has zero topological entropy,then for any xECR(f)--P(f) the w-limit set of x is an infinite minimal set. 相似文献
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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. 相似文献
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Fuzzy集的偏熵与关联熵 总被引:4,自引:0,他引:4
在文献[1]的基础上,推广模糊熵的概念。首次定义Fuzzy集的偏熵、关联熵和关联熵系数等新概念。对其主要性质进行讨论,并与模糊散度建立联系.得到一些重要结果。 相似文献
13.
K. B. Athreya 《Proceedings Mathematical Sciences》2009,119(4):531-539
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii)
in the class of all pdf f that satisfy ∝ fh
i
dμ = λ
i
for i = 1, 2, ..., ... kthe maximizer of entropy is an f
0 that is proportional to exp(Σc
i
h
i
) for some choice of c
i
. An extension of this to a continuum of constraints and many examples are presented. 相似文献
14.
Free Entropy 总被引:1,自引:0,他引:1
Free entropy is the analogue of entropy in free probabilitytheory. The paper is a survey of free entropy, its applicationsto von Neumann algebras and its connections to random matrixtheory, as well as a discussion of open problems and of a basicvariational problem, connected to random multimatrix models. 相似文献
15.
Christoph Kawan 《PAMM》2011,11(1):817-818
In this paper, the concept of invariance entropy for continuous-time control systems is introduced. This quantity measures the minimal data rate necessary to render a compact subset of the state space invariant by a coder-controller device. Invariance entropy is an intrinsic quantity of the open-loop system and shares several properties with the classical entropy quantities in the field of dynamical systems. Some of these properties, in particular relations to Lyapunov exponents, are pointed out. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Entropy of bi-capacities 总被引:1,自引:0,他引:1
In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a very natural interpretation in terms of the Choquet integral and satisfies many natural properties that one would expect from an entropy measure. 相似文献
18.
Vera Koponen 《Archive for Mathematical Logic》2009,48(6):515-522
A probability distribution can be given to the set of isomorphism classes of models with universe {1, ..., n} of a sentence in first-order logic. We study the entropy of this distribution and derive a result from the 0–1 law for first-order
sentences.
相似文献
19.
A. E. Litvak V. D. Milman A. Pajor N. Tomczak-Jaegermann 《Functional Analysis and Its Applications》2006,40(4):298-303
We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the extension property of ?∞. The second one, which can be called an “entropy lifting theorem,” provides estimates in terms of entropies of projections. 相似文献
20.
Entropy structure 总被引:2,自引:0,他引:2
Tomasz Downarowicz 《Journal d'Analyse Mathématique》2005,96(1):57-116
Investigating the emergence of entropy on different scales, we propose an “entropy structure” as a kind of master invariant
for the entropy theory of topological dynamical systems. An entropy structure is a sequence of functionsh
k on the simplex of invariant measures which converges to the entropy functionh and which falls into a distinguished equivalence class defined by a natural equivalence relation capturing the “type of nonuniformity
in convergence”. An entropy structure recovers several existing invariants, including the symbolic extension entropy hsex and the Misiurewicz parameter h*. Entropy theories of Misiurewicz, Katok, Brin—Katok, Newhouse, Romagnoli, Ornstein—Weiss and others all yield candidate sequences
(h
k); we determine which of these exhibit the correct type of convergence and hence become entropy structures. One of the satisfactory
sequences arises from a new treatment of entropy theory strictly in terms of continuous functions (in place of partitions
or covers). The results allow the computation of symbolic extension entropy without reference to zero dimensional extensions.
New light is shed on the property of asymptotich-expansiveness.
Supported by the KBN grant 2 P03 A 04622. 相似文献