共查询到20条相似文献,搜索用时 15 毫秒
1.
A. Lasota and J. A. Yorke proved that a piecewise expanding interval map admits finitely many ergodic absolutely continuous invariant probability measures. We generalize this to the random composition of such maps under conditions which are natural and less restrictive than those previously studied by Morita and Pelikan. For instance our conditions are satisfied in the case of arbitrary random -transformations, i.e., on where is chosen according to any stationary stochastic process (in particular, not necessarily i.i.d.) with values in .
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2.
Pawe? Góra 《Journal of Mathematical Analysis and Applications》2006,317(1):257-270
We consider a random map T=T(Γ,ω), where Γ=(τ1,τ2,…,τK) is a collection of maps of an interval and ω=(p1,p2,…,pK) is a collection of the corresponding position dependent probabilities, that is, pk(x)?0 for k=1,2,…,K and . At each step, the random map T moves the point x to τk(x) with probability pk(x). For a fixed collection of maps Γ, T can have many different invariant probability density functions, depending on the choice of the (weighting) probabilities ω. Most of the results in this paper concern random maps where Γ is a family of piecewise linear semi-Markov maps. We investigate properties of the set of invariant probability density functions of T that are attainable by allowing the probabilities in ω to vary in a certain class of functions. We prove that the set of all attainable densities can be determined algorithmically. We also study the duality between random maps generated by transformations and random maps constructed from a collection of their inverse branches. Such representation may be of greater interest in view of new methods of computing entropy [W. S?omczyński, J. Kwapień, K. ?yczkowski, Entropy computing via integration over fractal measures, Chaos 10 (2000) 180-188]. 相似文献
3.
O. Safronov 《Journal of Functional Analysis》2008,255(3):755-767
We consider an elliptic random operator, which is the sum of the differential part and the potential. The potential considered in the paper is the same as the one in the Andersson model, however the differential part of the operator is different from the Laplace operator. We prove that such an operator has absolutely continuous spectrum on all of (0,∞). 相似文献
4.
Let I=[0,1] and let P be a partition of I into a finite number of intervals. Let τ1, τ2; I→I be two piecewise expanding maps on P . Let G⊂I×I be the region between the boundaries of the graphs of τ1 and τ2. Any map τ:I→I that takes values in G is called a selection of the multivalued map defined by G . There are many results devoted to the study of the existence of selections with specified topological properties. However, there are no results concerning the existence of selection with measure-theoretic properties. In this paper we prove the existence of selections which have absolutely continuous invariant measures (acim). By our assumptions we know that τ1 and τ2 possess acims preserving the distribution functions F(1) and F(2). The main result shows that for any convex combination F of F(1) and F(2) we can find a map η with values between the graphs of τ1 and τ2 (that is, a selection) such that F is the η-invariant distribution function. Examples are presented. We also study the relationship of the dynamics of our multivalued maps to random maps. 相似文献
5.
《随机分析与应用》2013,31(5):983-994
Abstract A random map is a discrete‐time dynamical system in which one of a number of transformations is randomly selected and applied in each iteration of the process. In this paper, we study random maps with position dependent probabilities on the interval. Sufficient conditions for the existence of absolutely continuous invariant measures for weakly convex and concave random maps with position dependent probabilities is the main result of this note. 相似文献
6.
《随机分析与应用》2013,31(4):1121-1130
Abstract A position dependent random map is a dynamical system consisting of a collection of maps such that, at each iteration, a selection of a map is made randomly by means of probabilities which are functions of position. Let f* be an invariant density of the position dependent random map T. We consider a model of small random perturbations 𝔗? of the random map T. For each ? > 0, 𝔗? has an invariant density function f ?. We prove that f ? → f* as ? → 0. 相似文献
7.
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from zero, we obtain finitely many ergodic absolutely continuous invariant probability measures, describing the asymptotics of almost every point. We also prove a similar result for higher-dimensional random non-uniformly expanding dynamical systems. The results are consequences of the construction of such measures for skew-products with essentially arbitrary base dynamics and asymptotic expansion along the fibers. In both cases our method deals with either critical o singular points for the random maps. 相似文献
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Benoît Saussol 《Israel Journal of Mathematics》2000,116(1):223-248
We investigate the existence and statistical properties of absolutely continuous invariant measures for multidimensional expanding
maps with singularities. The key point is the establishment of a spectral gap in the spectrum of the transfer operator. Our
assumptions appear quite naturally for maps with singularities. We allow maps that are discontinuous on some extremely wild
sets, the shape of the discontinuities being completely ignored with our approach. 相似文献
11.
Masato Tsujii 《Inventiones Mathematicae》2001,143(2):349-373
We prove the existence of absolutely continuous invariant measures for arbitrary expanding piecewise linear maps on bounded
polyhedral domains in Euclidean spaces ℝ
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Oblatum 6-V-1999 & 8-VI-2000?Published online: 11 October 2000 相似文献
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I. N. Pankratova 《Siberian Mathematical Journal》2009,50(1):107-116
We consider the dynamical system that is determined by a multidimensional map with scalar type nonlinearity and a nonnegative matrix of special form. For this map we establish the bifurcation character for the location of cyclic invariant sets in the phase space of the system, determine their location and periods depending on the properties of the matrix. 相似文献
14.
FENGJINGHAI 《高校应用数学学报(英文版)》1997,12(3):363-370
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. 相似文献
15.
This paper investigates the matrix Dirac systems. Under some conditions on the potential matrices, it is shown that the spectrum of the Dirac operator is purely absolutely continuous outside the gaps containing the eigenvalues of q. 相似文献
16.
Tomasz Bielaczyc Katarzyna Horbacz 《Mathematical Methods in the Applied Sciences》2016,39(14):3947-3960
We consider continuous random dynamical systems with jumps. We estimate the dimension of the invariant measures and apply the results to a model of stochastic gene expression. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
N. Shahzad 《Mathematical and Computer Modelling》2005,41(13):1431-1436
We prove some random fixed-point theorems for random maps which are not necessarily continuous. This may lead to the discovery of some new results in random fixed-point theory for discontinuous maps. 相似文献
18.
Uri Kaluzhny 《Journal of Functional Analysis》2011,260(4):1029-1044
We consider random self-adjoint Jacobi matrices of the form
(Jωu)(n)=an(ω)u(n+1)+bn(ω)u(n)+an−1(ω)u(n−1) 相似文献
19.
We show that if an iterated function system with place-dependent probabilities admits an invariant and attractive measure, then it has the structure of a random dynamical system (in the sense of Ludwig Arnold). 相似文献
20.
Paweł Płonka 《随机分析与应用》2018,36(3):521-533
Tomasz Szarek presented interesting criteria for the existence of invariant measures and asymptotic stability of Markov operators on Polish spaces. Hans Crauel in his book presented the theory of random probabilistic measures on Polish spaces showing that notions of compactness and tightness for such measures are in one-to-one correspondence with such notions for non-random measures on Polish spaces, in addition to the criteria under which the space of random measures is itself a Polish space. This result allowed the transfer of results of Szarek to the case of random dynamical systems in the sense of Arnold. These criteria are interesting because they allow to use the existence of simple deterministic Lyapunov type function together with additional conditions to show the existence of invariant measures and asymptotic stability of random dynamical systems on general Polish spaces. 相似文献