共查询到20条相似文献,搜索用时 15 毫秒
1.
L. Olsen 《Bulletin des Sciences Mathématiques》2008,132(8):650-678
During the past 10 years multifractal analysis has received an enormous interest. For a sequence n(φn) of functions on a metric space X, multifractal analysis refers to the study of the Hausdorff and/or packing dimension of the level sets(1) of the limit function limnφn. However, recently a more general notion of multifractal analysis, focusing not only on points x for which the limit limnφn(x) exists, has emerged and attracted considerable interest. Namely, for a sequence n(xn) in a metric space X, we let A(xn) denote the set of accumulation points of the sequence n(xn). The problem of computing that the Hausdorff dimension of the set of points x for which the set of accumulation points of the sequence (φnn(x)) equals a given set C, i.e. computing the Hausdorff dimension of the set(2) {x∈X|A(φn(x))=C} has recently attracted considerable interest and a number of interesting results have been obtained. However, almost nothing is known about the packing dimension of sets of this type except for a few special cases investigated in [I.S. Baek, L. Olsen, N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007) 267–287]. The purpose of this paper is to compute the packing dimension of those sets for a very general class of maps φn, including many examples that have been studied previously, cf. Theorem 3.1 and Corollary 3.2. Surprisingly, in many cases, the packing dimension and the Hausdorff dimension of the sets in (2) do not coincide. This is in sharp contrast to well-known results in multifractal analysis saying that the Hausdorff and packing dimensions of the sets in (1) coincide. 相似文献
2.
Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:
3.
R. Nair 《Indagationes Mathematicae》2004,15(3):373-381
Given a subset S of Z and a sequence I = (In)n=1∞ of intervals of increasing length contained in Z, let
4.
C.G.J. Roettger 《Journal of Number Theory》2005,113(1):69-83
Ledrappier introduced the following type of space of doubly indexed sequences over a finite abelian group G,
5.
W.A. Kirk 《Journal of Mathematical Analysis and Applications》2003,277(2):645-650
Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies
6.
Xiongping Dai 《Journal of Differential Equations》2006,225(2):549-572
In this paper, the author considers, by Liao methods, the stability of Lyapunov exponents of a nonautonomous linear differential equations: with linear small perturbations. It is proved that, if A(t) is a upper-triangular real n by n matrix-valued function on R+, continuous and uniformly bounded, and if there is a relatively dense sequence in R+, say 0=T0<T1<?<Ti<?, such that
7.
Milena Chermisi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(3):695-703
In Rm×Rn−m, endowed with coordinates X=(x,y), we consider the PDE
8.
Feng Tan 《Topology and its Applications》2011,158(3):533-541
9.
Fernanda Botelho James E. Jamison 《Journal of Mathematical Analysis and Applications》2011,381(2):821-832
For a Banach space E and a compact metric space (X,d), a function F:X→E is a Lipschitz function if there exists k>0 such that
10.
Marcy Barge 《Topology and its Applications》2007,154(17):3095-3099
Suppose Tφ and Tθ are tiling spaces arising from primitive nonperiodic substitutions φ and θ. Suppose Fφ and Fθ denote the corresponding inflation and substitution maps on the respective tiling spaces. We prove that Tφ and Tθ are homeomorphic if and only if there exist positive integers m and n such that and are topologically conjugate. 相似文献
11.
Marek Cezary Zdun 《Journal of Mathematical Analysis and Applications》2008,342(1):340-348
We prove that for every orientation-preserving homeomorphism possessing periodic points of order n there exist a homeomorphism such that Tn=id and a homeomorphism without periodic points except fixed points such that
F=Tq○G 相似文献
12.
Biagio Ricceri 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4151-4157
If X is a real Banach space, we denote by WX the class of all functionals possessing the following property: if {un} is a sequence in X converging weakly to u∈X and lim infn→∞Φ(un)≤Φ(u), then {un} has a subsequence converging strongly to u.In this paper, we prove the following result:Let X be a separable and reflexive real Banach space; an interval; a sequentially weakly lower semicontinuous C1 functional, belonging to WX, bounded on each bounded subset of X and whose derivative admits a continuous inverse on X∗; a C1 functional with compact derivative. Assume that, for each λ∈I, the functional Φ−λJ is coercive and has a strict local, not global minimum, say .Then, for each compact interval [a,b]⊆I for which , there exists r>0 with the following property: for every λ∈[a,b] and every C1 functional with compact derivative, there exists δ>0 such that, for each μ∈[0,δ], the equation
Φ′(x)=λJ′(x)+μΨ′(x) 相似文献
13.
Farid Madani 《Bulletin des Sciences Mathématiques》2008,132(7):575
Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation
14.
15.
Pierre Gillibert 《Journal of Pure and Applied Algebra》2010,214(8):1306-1318
We denote by the semilattice of all compact congruences of an algebra A. Given a variety V of algebras, we denote by the class of all semilattices isomorphic to for some A∈V. Given varieties V and W of algebras, the critical point of V under W is defined as . Given a finitely generated variety V of modular lattices, we obtain an integer ?, depending on V, such that for any n≥? and any field F.In a second part, using tools introduced in Gillibert (2009) [5], we prove that:
16.
M.C. Zdun 《Journal of Mathematical Analysis and Applications》2007,330(1):51-65
We give a necessary and sufficient condition for topological conjugacy of homeomorphisms of the circle having periodic points. As an application we get the following theorem on the representation of homeomorphisms. The homeomorphism has a periodic point of period n iff there exist a positive integer q<n relatively prime to n and a homeomorphism such that the lift of Φ−1○F○Φ restricted to [0,1] has the form
17.
Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings 总被引:1,自引:0,他引:1
Lin Wang 《Journal of Mathematical Analysis and Applications》2006,323(1):550-557
Suppose that K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E. Let be two nonself asymptotically nonexpansive mappings with sequences {kn},{ln}⊂[1,∞), limn→∞kn=1, limn→∞ln=1, , respectively. Suppose {xn} is generated iteratively by
18.
Let X={Xt,t?0} be a symmetric Markov process in a state space E and D an open set of E. Denote by XD the subprocess of X killed upon leaving D. Let S={St,t?0} be a subordinator with Laplace exponent φ that is independent of X. The processes Xφ?{XSt,t?0} and are called the subordinate processes of X and XD, respectively. Under some mild conditions, we show that, if {-μn,n?1} and {-λn,n?1} denote the eigenvalues of the generators of the subprocess of Xφ killed upon leaving D and of the process XD respectively, then
19.
Jiang Ye 《Journal of Mathematical Analysis and Applications》2007,327(1):695-714
Let be a sequence of i.i.d. random variables with EX=0 and EX2=σ2<∞. Set , Mn=maxk?n|Sk|, n?1. Let r>1, then we obtain
20.
It is known that for any nonzero complex n×n matrices X and Y the quotient of Frobenius norms