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1.
Generic properties of invariant measures for continuous piecewise monotonic transformations 总被引:4,自引:0,他引:4
Franz Hofbauer 《Monatshefte für Mathematik》1988,106(4):301-312
We endow the set of all invariant measures of topologically transitive subsetsL withh
top (L)>0 of a continuous piecewise monotonic transformation on [0, 1] with the weak topology. We show that the set of periodic orbit measures is dense, that the sets of ergodic, of nonatomic, and of measures with supportL are denseG
-sets, that the set of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a denseG
-set. 相似文献
2.
We study the doubling property of binomial measures on the middle interval Cantor set. We obtain a necessary and sufficient
condition that enables a binomial measure to be doubling. Then we determine those doubling binomial measures which can be
extended to be doubling on [0,1]. Finally, we construct a compact set X in [0,1] and a doubling measure μ on X, such that [`(F)]X=X\overline{F}_{X}=X and m|EX{\mu|}_{E_{X}} is doubling on E
X
, where E
X
is the set of accumulation points of X and F
X
is the set of isolated points of X. 相似文献
3.
Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set M
G
. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of M
G
. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify nonnegatively
curved fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected
4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure. 相似文献
4.
Let X be a locally compact metric space. One important object connected with the distribution behavior of an arbitrary sequence x on X is the set M( x ) of limit measures of x . It is defined as the set of accumulation points of the sequence of the discrete measures induced by x . Using binary representation of reals one gets a natural bijective correspondence between infinite subsets of the set ℕ of positive integers and numbers in the unit interval I = 〈0, 1]. Hence to each sequence x = (xn)n∈ℕ ∈ Xℕ and every a I there corresponds a subsequence denoted by a x . We investigate the set M(a x ) for given x with emphasis on the behavior for “typical” a in the sense of Baire category, Lebesgue measure and Hausdorff dimension. 相似文献
5.
Franz Hofbauer 《Israel Journal of Mathematics》1979,34(3):213-237
We consider a class of piecewise monotonically increasing functionsf on the unit intervalI. We want to determine the measures with maximal entropy for these transformations. In part I we construct a shift-space Σ
f
+
isomorphic to (I, f) generalizing the \-shift and another shift Σ
M
over an infinite alphabet, which is of finite type given by an infinite transition matrixM. Σ
M
has the same set of maximal measures as (I, f) and we are able to compute the maximal measures of maximal measures of. In part II we try to bring these results back to
(I, f). There are only finitely many ergodic maximal measures for (I, f). The supports of two of them have at most finitely many points in common. If (I, f) is topologically transitive it has unique maximal measure. 相似文献
6.
《Quaestiones Mathematicae》2013,36(4):473-481
We define strong and weak affinities of a number a for a sequence (xk ) denoted by L (a,(xk )) and U (a, (xk )) respectively. We show U (a,(xk )) > 0 if and only if the number a is a statistical limit point of the sequence (xk ). We consider the distribution of sequences with positive weak and strong measures of affinity within the space l ∞ of bounded sequences. The main result is that the set of bounded sequences with U (a,(xk )) > 0, that is, the set of sequences with statistical limit points, is a dense subset in l ∞ of the first category. We also show the set of sequences with positive strong affinities is a nowhere dense subset of l ∞. 相似文献
7.
We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding
to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for
a Cayley tree of order four, there exist critical values T
c
< T
cr
of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < T
c
or T > T
cr
, three weakly periodic Gibbs measures for T = T
c
, and one weakly periodic Gibbs measure for T
c
< T ≤ T
cr
.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 292–302, August, 2008. 相似文献
8.
Pedro Nicolás 《Journal of Pure and Applied Algebra》2008,212(12):2633-2659
Curved A∞-algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A∞-algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras via the bar construction and produce Quillen model structures on their module categories. We define the analogue of the relative derived category for a curved dg algebra. 相似文献
9.
Wolfgang Weil 《Geometriae Dedicata》1980,9(3):299-306
The set L
j of jth-order surface area measures of convex bodies in d-space is well known for j=d–1. A characterization of L
j was obtained by Firey and Berg. The determination of L
j, for j{2, ..., d–2}, is an open problem. Here we show some properties of L
j concerning convexity, closeness, and size. Especially we prove that the difference set L
j–L
j is dense (in the weak topology) in the set of signed Borel measures on the unit sphere which have barycentre 0. 相似文献
10.
Let M
n
denote the n-th moment space of the set of all probability measures on the interval [0, 1], P
n
the uniform distribution on the set M
n
and r
n + 1 the maximal range of the (n + 1)-th moments corresponding to a random moment point C
n
with distribution P
n
on M
n
. We study several asymptotic properties of the stochastic process (r
⌊nt⌋+1)
t∈[0,T] if n → ∞. In particular weak convergence to a Gaussian process and a large deviation principle are established.
相似文献
11.
Paul J. Tanenbaum 《Journal of Graph Theory》1999,32(2):171-190
We characterize the pairs (G1, G2) of graphs on a shared vertex set that are intersection polysemic: those for which the vertices may be assigned subsets of a universal set such that G1 is the intersection graph of the subsets and G2 is the intersection graph of their complements. We also consider several special cases and explore bounds on the size of the universal set. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 171–190, 1999 相似文献
12.
Summary Under investigation are measures m defined on a σ-algebraA with range in a Banach space X having a Schauder basis {xn}. Utilizing the corresponding coefficient functionals and coefficient measures, we study the interaction between properties
for these measures and properties for the existing measure m. For the spaceCA(A, X) of all countably additive measures of finite variation fromA into X, we show that certain separable subspaces of it are isomorphic-isometric with certain separable subspaces of functions
of bounded variation on the interval [0, 1]. For {vn} inCA(A, X) such that {vn(A)} converges to v(A) for all A εA a certain ? control measure ? is constructed. An integral for set functions relative to a measure is defined and necessary
and sufficient conditions are given for weak convergence. Bounded operators on the space FAC(A,R) of finitelly additive scalar valued set functions onA which are absolutely continuous with respect to λ are considered. Necessary and sufficient conditions for continuity and
for compactness are given for Banach space valued operators T defined on such spaces. Weak compactness of T is also studied.
Finally, a different kind of representation is given for Banach space valued operators defined on the space FAv(A, X) of finitely additive set functions fromA into X.
Entrata in Redazione il 26 novembre 1976.
The first author expresses his gratitude to the Italian Consiglio Nazionale delle Ricerche and the Università degli Studi
di Param for the support of his work during his tenure as Visiting Professor of Mathematics. This work was supported by NATO
Research Grant No. 835. 相似文献
13.
V. Stakėnas 《Lithuanian Mathematical Journal》2006,46(2):208-216
Let Q
+ denote the set of positive rational numbers. We define discrete probability measures ν
x
on the σ-algebra of subsets of Q
+.We introduce additive functions ƒ: Q
+ → G and obtain a bound for νx(ƒ (r) ∉ X+X−X) using a probability related to some independent random variables. This inequality is an analogue to that proved by I. Ruzsa
for additive arithmetical functions.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 256–266, April–June, 2006. 相似文献
14.
We investigate random interlacements on ?d, d ≥ 3. This model, recently introduced in [8], corresponds to a Poisson cloud on the space of doubly infinite trajectories modulo time shift tending to infinity at positive and negative infinite times. A nonnegative parameter u measures how many trajectories enter the picture. Our main interest lies in the percolative properties of the vacant set left by random interlacements at level u. We show that for all d ≥ 3 the vacant set at level u percolates when u is small. This solves an open problem of [8], where this fact has only been established when d ≥ 7. It also completes the proof of the nondegeneracy in all dimensions d ≥ 3 of the critical parameter u* of [8]. © 2008 Wiley Periodicals, Inc. 相似文献
15.
A. D. Baranov 《Journal of Mathematical Sciences》2000,101(2):2881-2913
The boundedness conditions for the differentiation operator in Hilbert spaces of entire functions (Branges spaces) and conditions
under which the embedding Kи⊂L2(μ) holds in spaces Kи associated with the Branges spacesH(E) are studied. Measure μ such that the above embedding is isometric are of special interest. It turns out that the condition
E'/E∈H∞(C+) is sufficient for the boundedness of the differentiation operator inH(E). Under certain restrictions on E, this condition is also necessary. However, this fact fails in the general case, which is
demonstrated by the counterexamples constructed in this paper. The convex structure of the set of measures μ such that the
embedding KE
*
/E⊂L2(μ) is isometric (the set of such measures was described by de Brages) is considered. Some classes of measures that are extreme
points in the set of Branges measures are distinguished. Examples of measures that are not extreme points are also given.
Bibliography: 7 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 27–68. 相似文献
16.
P. J. Fitzsimmons 《Probability Theory and Related Fields》1990,84(2):251-265
Summary We examine three of the principles of probabilistic potential theory in a nonclassical setting. These are: (i) the bounded maximum principle, (ii) the positive definiteness of the energy (of measures of bounded potential), and (iii) the condition that each semipolar set is polar. These principles are known to be equivalent in the context of two Markov processes in strong duality, when excessive functions are lower semicontinuous. We show that when the principles are appropriately formulated their equivalence persists in the wider context of a Borel right Markov processX with distinguished excessive measurem. We make no duality hypotheses andm need not be a reference measure. Our main tools are the stationary process (Y, Q
m) associated withX andm, and a correspondence between potentials U and certain random measures over (Y, Q
m).Research supported in part by NSF Grant 8419377 相似文献
17.
We consider p independent Brownian motions in \input amssym ${\Bbb R}^d$ . We assume that p ≥ 2 and p (d ? 2) < d. Let ?t denote the intersection measure of the p paths by time t, i.e., the random measure on \input amssym ${\Bbb R}^d$ that assigns to any measurable set \input amssym $A \subset {\Bbb R}^d$ the amount of intersection local time of the motions spent in A by time t. Earlier results of X. Chen derived the logarithmic asymptotics of the upper tails of the total mass \input amssym $\ell _t \left({{\Bbb R}^d } \right)$ as t → ∞. In this paper, we derive a large‐deviation principle for the normalized intersection measure t?p?t on the set of positive measures on some open bounded set \input amssym $B \subset {\Bbb R}^d$ as t → ∞ before exiting B. The rate function is explicit and gives some rigorous meaning, in this asymptotic regime, to the understanding that the intersection measure is the pointwise product of the densities of the normalized occupation times measures of the p motions. Our proof makes the classical Donsker‐Varadhan principle for the latter applicable to the intersection measure. A second version of our principle is proved for the motions observed until the individual exit times from B, conditional on a large total mass in some compact set . This extends earlier studies on the intersection measure by König and Mörters. © 2012 Wiley Periodicals, Inc. 相似文献
18.
Michael Molloy 《Random Structures and Algorithms》2014,45(3):498-512
–We consider two random graphs G1, G2, both on the same vertex set. We ask whether there is a non‐trivial set of vertices S, so that S induces a connected subgraph both in G1 and in G2. We determine the threshold for the appearance of such a subset, as well as the size of the largest such subset. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 45, 498–512, 2014 相似文献
19.
Jeff Edmonds 《Discrete and Computational Geometry》2008,39(4):747-765
We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair
within a set of n points) into ℝ2 Cartesian space preserving their l
∞ (or l
1) metric distances. Its expected time is
(i.e., within a poly-log of the size of the input) beating the previous
algorithm. In contrast, we prove that detecting l
∞3 embeddings is NP-complete. The problem is also NP-complete within l
12 or l
∞2 with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are
curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded
in l
∞3; however, it can be embedded if any single point is removed.
This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper. 相似文献
20.
Arthur W. Apter 《Mathematical Logic Quarterly》2001,47(1):35-44
We prove two theorems which in a certain sense show that the number of normal measures a measurable cardinal κ can carry is independent of a given fixed behavior of the continuum function on any set having measure 1 with respect to every normal measure over κ . First, starting with a model V ⊨ “ZFC + GCH + o(κ) = δ*” for δ* ≤ κ+ any finite or infinite cardinal, we force and construct an inner model N ⊆ V [G] so that N ⊨ “ZF + (∀δ < κ) [DCδ] + ¬ACκ + κ carries exactly δ* normal measures + 2δ = δ++ on a set having measure 1 with respect to every normal measure over κ”. There is nothing special about 2δ = δ here, and other stated values for the continuum function will be possible as well. Then, starting with a modelV ⊨ “ZFC + GCH + κis supercompact”, we force and construct models of AC in which, roughly speaking, regardless of the specified behavior of the continuum function below κ on any set having measure 1 with respect to every normal measure over κ, κ can in essence carry any number of normal measures δ* ≥ κ++. 相似文献