共查询到20条相似文献,搜索用时 31 毫秒
1.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
2.
周云华 《数学物理学报(B辑英文版)》2011,31(1):102-108
Let T : X → X be a uniformly continuous homeomorphism on a non-compact metric space (X, d). Denote by X* = X ∪ {x*} the one point compactification of X and T * : X* → X* the homeomorphism on X* satisfying T *|X = T and T *x* = x*. We show that their topological entropies satisfy hd(T, X) ≥ h(T *, X*) if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space. 相似文献
3.
Amos Nevo 《Israel Journal of Mathematics》1991,75(1):1-19
We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of
ends, Ω
X
. For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω
X
→ Ω
T
, and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs
are discussed, as well as some examples. 相似文献
4.
Absolute continuities of exit measures for superdiffusions 总被引:3,自引:0,他引:3
REN Yanxia 《中国科学A辑(英文版)》2000,43(5):449-457
Suppose X= Xt, XT, Pμis a superdiffusion in ℝd with general branching mechanism ψ and general branching rate functionA. We discuss conditions onA to guarantee that the exit measure XTL of the superdiffusionX from bounded smooth domains in ℝd have absolutely continuous states. 相似文献
6.
R. A. McCoy 《Mathematica Slovaca》2010,60(4):541-570
We introduce a lower semicontinuous analog, L
−(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements
of L
−(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L
−(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part
I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L
−(X) and L
−(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal
spaces X and Y, every ordered homeomorphism between L
−(X) and L
−(Y) can be characterized by a unique factorization. 相似文献
7.
A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T
2∥ = 1+∥T
2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis
and that the infimum of diameters of the slices of its unit ball is positive. 相似文献
8.
On weak positive supercyclicity 总被引:1,自引:0,他引:1
A bounded linear operator T on a separable complex Banach space X is called weakly supercyclic if there exists a vector x ∈ X such that the projective orbit {λT
n
x: n ∈ ℕ λ ∈ ℂ} is weakly dense in X. Among other results, it is proved that an operator T such that σ
p
(T
*) = 0, is weakly supercyclic if and only if T is positive weakly supercyclic, that is, for every supercyclic vector x ∈ X, only considering the positive projective orbit: {rT
n
x: n ∈ ℂ, r ∈ ℝ+} we obtain a weakly dense subset in X. As a consequence it is established the existence of non-weakly supercyclic vectors (non-trivial) for positive operators
defined on an infinite dimensional separable complex Banach space. The paper is closed with concluding remarks and further
directions.
Partially supported by MEC MTM2006-09060 and MTM2006-15546, Junta de Andalucía FQM-257 and P06-FQM-02225.
Partially supported by Junta de Andalucía FQM-257, and P06-FQM-02225 相似文献
9.
10.
Sébastien Ferenczi 《Israel Journal of Mathematics》1982,42(4):334-342
Ergodic theory: for every dynamical system (X,A,T, μ), totally ergodic and of finite entropy, there exist a sequenceS of integers, of upper density zero, and a partitionQ ofX, such that V
i∈S
T
−i Q is the whole σ-algebraA. Furthermore, there is a “universal” sequenceS
0 for which this property is true if we restrict ourselves to the class of strongly mixing systems.
相似文献
11.
For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the
associated crossed product C
*-algebras C(X)⋊
α,ℒℕ introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological
freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In
this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering
map is topologically free; the canonical embedding of C(X) into C(X)⋊
α,ℒℕ is a maximal abelian C
*-subalgebra of C(X)⋊
α,ℒℕ; any nontrivial two sided ideal of C(X)⋊
α,ℒℕ has non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊
α,ℒℕ is faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product
C
*-algebras of homeomorphism dynamical systems. 相似文献
12.
We prove that if X denotes the interval or the circle then every transformation T:X→X of class C
r
, where r>1 is not necessarily an integer, admits a symbolic extension, i.e., every such transformation is a topological factor of
a subshift over a finite alphabet. This is done using the theory of entropy structure. For such transformations we control
the entropy structure by providing an upper bound, in terms of Lyapunov exponents, of local entropy in the sense of Newhouse
of an ergodic measure ν near an invariant measure μ (the antarctic theorem). This bound allows us to estimate the so-called
symbolic extension entropy function on invariant measures (the main theorem), and as a consequence, to estimate the topological
symbolic extension entropy; i.e., a number such that there exists a symbolic extension with topological entropy arbitrarily
close to that number. This last estimate coincides, in dimension 1, with a conjecture stated by Downarowicz and Newhouse [13,
Conjecture 1.2]. The passage from the antarctic theorem to the main theorem is applicable to any topological dynamical system,
not only to smooth interval or circle maps. 相似文献
13.
Let T be a continuous map on a compact metric space (X, d). A pair of distinct points x, y ∈ X is asymptotic if lim n→∞ d(T n x, T n y) = 0. We prove the following four conditions to be equivalent: 1. h top(T) = 0; 2. (X, T) has a (topological) extension (Y,S) which has no asymptotic pairs; 3. (X, T) has a topological extension (Y ′, S′) via a factor map that collapses all asymptotic pairs; 4. (X, T) has a symbolic extension (i.e., with (Y ′, S′) being a subshift) via a map that collapses asymptotic pairs. The maximal factors (of a given system (X, T)) corresponding to the above properties do not need to coincide. 相似文献
14.
I. Juhász 《Israel Journal of Mathematics》1993,81(3):369-379
The weight-spectrumSp(w, X) of a spaceX is the set of weights of all infinite closed subspaces ofX. We prove that ifκ>ω is regular andX is compactT
2 withω(X)≥κ then some λ withκ≤λ≤2<κ is inSp(ω, X). Under CH this implies that the weight spectrum of a compact space can not omitω
1, and thus solves problem 22 of [M]. Also, it is consistent with 2ω=c being anything it can be that every countable closed setT of cardinals less thanc withω ∈ T satisfiesSp(w, X)=T for some separable compact LOTSX. This shows the independence from ZFC of a conjecture made in [AT].
Research supported by OTKA grant no. 1908. 相似文献
15.
Eli Glasner 《Journal d'Analyse Mathématique》1994,64(1):241-262
For a minimal distal flow (X, T) and a positive integern, let be the largest distal factor of ordern. The existence of a denseG
δ subset ω ofX is shown, such that forx ∈ ω the orbit closure of (x,x,...,x) ∈ X
n+1 under τ =T ×T
2 ... ×T
n+1 is π-saturated. In fact, an analogous statement for a general minimal flow is proved in terms of its PI-tower. On the way
we get some topological “ergodic” decomposition theorems. 相似文献
16.
Kevin McGoff 《Journal d'Analyse Mathématique》2011,114(1):157-206
For a continuous self-map T of a compact metrizable space with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the theory of entropy structure and symbolic extensions. Given any compact manifold
M and any countable ordinal α, we construct a continuous, surjective self-map ofM having order of accumulation of entropy α. If the dimension of M is at least 2, then the map can be chosen to be a homeomorphism. 相似文献
17.
Suppose X and Y are Polish spaces with non-atomic Borel probability measures μ and ν and suppose that T and S are ergodic measure-preserving homeomorphisms of (X, μ) and (Y, ν). Then there are invariant G
δ
subsets X′ ⊂ X and Y′ ⊂ Y of full measure and a homeomorphism ϕ: X′ → Y′ which maps μ|X′ to ν|Y′ and maps T-orbits onto S-orbits. We also deal with the case where T and S preserve infinite invariant measures. 相似文献
18.
Consider (X,F, μ,T) a Lebesgue probability space and measure preserving invertible map. We call this a dynamical system. For a subsetA ∈F. byT
A:A →A we mean the induced map,T
A(x)=TrA(x)(x) wherer
A(x)=min{i〉0:T
i(x) ∈A}. Such induced maps can be topologized by the natural metricD(A, A’) = μ(AΔA’) onF mod sets of measure zero. We discuss here ergodic properties ofT
A which are residual in this metric. The first theorem is due to Conze.Theorem 1 (Conze):For T ergodic, T
A is weakly mixing for a residual set of A.Theorem 2:For T ergodic, 0-entropy and loosely Bernoulli, T
A is rank-1, and rigid for a residual set of A.Theorem 3:For T ergodic, positive entropy and loosely Bernoulli, T
A is Bernoulli for a residual set of A.Theorem 4:For T ergodic of positive entropy, T
A is a K-automorphism for a residual set of A.
A strengthening of Theorem 1 asserts thatA can be chosen to lie inside a given factor algebra ofT. We also discuss even Kakutani equivalence analogues of Theorems 1–4. 相似文献
19.
Jin Chuan HOU Xiu Ling ZHANG 《数学学报(英文版)》2006,22(1):179-186
Let X be an infinite-dimensional complex Banach space and denote by B(X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B(X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B(X) such that either Φ(T) = cATA^-1 + ψ(T)I for all T, or Φ(T) = cAT*A^-1 + ψ(T)I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero. 相似文献
20.
Jun Tomiyama 《Acta Appl Math》2009,108(3):561-572
For the homeomorphism C*-algebra A(Σ) arising from a topological dynamical system Σ=(X,σ) where σ is a homeomorphism on an arbitrary compact Hausdorff space X, we first give detailed classification of its closed ideals into four classes. In case when X is a compact metric space, we then determine the conditions when the quotient algebras of A(Σ) become quasidiagonal. The case of A(Σ) itself was treated by M. Pimsner. 相似文献