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1.
Regularity and other properties of absolutely continuous invariant measures for the quadratic family
In the current paper we study in more detail some properties of the absolutely continuous invariant measures constructed in the course of the proof of Jakobson's Theorem. In particular, we show that the density of the invariant measure is continuous at Misiurewicz points. From this we deduce that the Lyapunov exponent is also continuous at these points (our considerations apply just to the parameters constructed in the proof of Jakobson's Theorem). Other properties, like the positivity of the Lyapunov exponent, uniqueness of the absolutely continuous invariant measure and exactness of the corresponding dynamical system, are also proved.This paper was written during the author's stay at the IAS while supported by NSF grant DMS-860 1978 相似文献
2.
Two widely used information measures are compared. It is shown that the Kullback measure, unlike the Shannon measure, provides the basis for a consistent theory of information which extends to continuous sample spaces and to nonconstant prior distributions. It is shown that the Kullback measure is a generalization of the Shannon measure, and that the Kullback measure has more reasonable additivity properties than does the Shannon measure. The results lend support to Jaynes's entropy maximization procedure. 相似文献
3.
Particle models with finitely many types of particles are considered, both on ℤ
d
and on discrete point sets of finite local complexity. Such sets include many standard examples of aperiodic order such as
model sets or certain substitution systems. The particle gas is defined by an interaction potential and a corresponding Gibbs
measure. Under some reasonable conditions on the underlying point set and the potential, we show that the corresponding diffraction
measure almost surely exists and consists of a pure point part and an absolutely continuous part with continuous density.
In particular, no singular continuous part is present. 相似文献
4.
Doug Pickrell 《Journal of Geometry and Physics》1996,19(4):315-367
For a given gauge group and compact Riemannian two-manifold, it is known that the associated Yang-Mills measure can be defined directly as a finitely additive measure on the space of connections, and this finitely additive measure is invariant with respect to SDiff, the group of all area-preserving diffeomorphisms of the surface. The first question we address is whether this symmetry essentially characterizes the projection of the Yang-Mills measure to the space of gauge equivalence classes. The proper formulation of this question entails the construction of an SDiff-equivariant equivariant completion of the space of continuous connections, such that the projection of the Yang-Mills measure to the space of gauge equivalence classes has a countably additive extension. We also consider the coupling of the Yang-Mills measure to determinants of Dirac operators. The basic problems are to prove that the coupled measure is absolutely continuous with respect to the background Yang-Mills measure, to find a reasonable formula for the Radon-Nikodym derivative, and to analyze the action of SDiff. 相似文献
5.
We prove that in the Euclidean representation of the three-dimensional massless Nelson model, the t = 0 projection of the interacting measure is absolutely continuous with respect to a Gaussian measure with a suitably adjusted mean. We also determine the Hamiltonian in the Fock space over this Gaussian measure space. 相似文献
6.
In this paper, we investigated measurement of quantum correlation for two mode continuous variable systems, and constructed two operators to measure quantum correlation of continuous variable systems. These operators not only can be criteria for quantum correlation, but also can be measurement for quantum correlation. 相似文献
7.
为了准确分析混沌序列的复杂性, 采用模糊熵算法(FuzzyEn) 对典型离散混沌系统和连续混沌系统的复杂度进行分析. 与近似熵(ApEn)、 样本熵(SampEn) 和强度统计复杂度算法相比, FuzzyEn算法是一种更有效的混沌复杂度测度算法, 且对相空间维数(m)、 相似容限度(r) 和序列长度(N) 的敏感性、 依赖性更低, 鲁棒性和测度值的连续性更好. 对混沌系统的复杂性分析表明, 连续混沌系统的复杂度远小于离散混沌系统, 但是如果利用高复杂度的离散混沌伪随机序列或经典 m序列对连续混沌系统产生的伪随机序列进行扰动, 则能大大提高混沌序列的复杂性. 为混沌序列在密码学和混沌保密通信中的应用提供了理论依据. 相似文献
8.
We consider a dynamical system with state space M, a smooth, compact subset of some R(n), and evolution given by T(t), x(t)=T(t)x, x in M; T(t) is invertible and the time t may be discrete, t in Z, T(t)=T(t), or continuous, t in R. Here we show that starting with a continuous positive initial probability density rho(x,0)>0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on R(n), the expectation value of logrho(x,t), with respect to any stationary (i.e., time invariant) measure nu(dx), is linear in t, nu(logrho(x,t))=nu(logrho(x,0))+Kt. K depends only on nu and vanishes when nu is absolutely continuous with respect to dx.(c) 1998 American Institute of Physics. 相似文献
9.
Tatiana Yarmola 《Communications in Mathematical Physics》2011,304(3):665-688
We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal,
heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely continuous with
respect to a Lebesgue-type reference measure and conclude that there exists at most one absolutely continuous steady state. 相似文献
10.
We study the invariant measure of a Markov chain obtained by randomly composing two rational maps related to the Anderson model with a Bernoulli potential. For a certain range of the parameters we show that the invariant measure is singular continuous. In certain cases the support turns out to be a Cantor set with a multifractal structure. 相似文献
11.
The Absolutely Continuous Spectrum of One-Dimensional Schrödinger Operators with Decaying Potentials
Christian Remling 《Communications in Mathematical Physics》1998,193(1):151-170
We investigate one-dimensional Schr?dinger operators with asymptotically small potentials. It will follow from our results
that if with , then is an essential support of the absolutely continuous part of the spectral measure. We also prove that if , then the spectrum is purely absolutely continuous on . These results are optimal.
Received: 25 June 1997 / Accepted: 29 July 1997 相似文献
12.
For a random field on a general discrete set, we introduce a condition that the range of the correlation from each site is within a predefined compact set D. For such a random field ?? defined on the model set ?? that satisfies a natural geometric condition, we develop a method to calculate the diffraction measure of the random field. The method partitions the random field into a finite number of random fields, each being independent and admitting the law of large numbers. The diffraction measure of ?? consists almost surely of a pure-point component and an absolutely continuous component. The former is the diffraction measure of the expectation E[??], while the inverse Fourier transform of the absolutely continuous component of ?? turns out to be a weighted Dirac comb which satisfies a simple formula. Moreover, the pure-point component will be understood quantitatively in a simple exact formula if the weights are continuous over the internal space of ??. Then we provide a sufficient condition that the diffraction measure of a random field on a model set is still pure-point. 相似文献
13.
J. Dieckmann 《General Relativity and Gravitation》1988,20(9):859-867
It is shown that on every spacetime there is a finite Borel measure such that open sets have positive measure and the topological boundary of the chronological past/future of every point has measure zero. Using this measure volume, functions are defined. It is shown that they are semicontinuous, and the set of points at which they are discontinuous is a union of nullgeodesics. The following causality conditions are characterized in terms of their properties: chronological, distinguishing, strongly causal, causally continuous, globally hyperbolic. 相似文献
14.
15.
V. M. Khatsymovsky 《Physics letters. [Part B]》2003,560(3-4):245-251
Regge calculus generalised to independent area tensor variables is considered. Continuous time limit is found and formal Feynman path integral measure corresponding to the canonical quantisation is written out. Quantum measure in the completely discrete theory is found which possesses the property to lead to the Feynman path integral in the continuous time limit whatever coordinate is chosen as the time. This measure can be well defined by passing to the integration over imaginary field variables (area tensors). Averaging with the help of this measure gives finite expectation values for areas. 相似文献
16.
17.
Paulo Varandas 《Journal of statistical physics》2012,146(2):330-358
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily
invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation
sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local
diffeomorphisms. For that purpose, a measure theoretical weak form of specification is introduced and proved to hold for the
robust classes of multidimensional non-uniformly expanding local diffeomorphisms and Viana maps. 相似文献
18.
利用斩波器将连续激光斩波成为脉冲宽度s量级重频脉冲激光,利用选单器将重频脉冲激光转变成单脉冲激光,从而实现变连续激光为单脉冲激光。由陷阱探测器测量连续激光的输出功率,高速APD、高增益PIN探测器作为波形探测器测量脉冲激光波形,并通过示波器对脉冲宽度进行测量。依据测量得到的功率和波形就可得到脉冲激光能量,从而实现了0.2 pJ激光微能量的测量和校准,通过不确定度分析,该装置的pJ激光能量测量不确定度达到了0.42%。 相似文献
19.
M. J. Westwater 《Communications in Mathematical Physics》1980,72(2):131-174
An existence theorem is proved for a probability measure on continuous paths in space, proposed by Edwards as a stochastic model for the geometric properties of long polymer chains. 相似文献
20.
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure. 相似文献