Tài liệu Đề tài " Metric attractors for smooth unimodal maps " docx

... Metric attractors for smooth unimodal maps By Jacek Graczyk, Duncan Sands, and Grzegorz ´Swia¸tek Annals of Mathematics, 159 (2004), 725–740 Metric attractors for smooth unimodal maps By ... interior and, for some n>0, f n (J) ⊆ J and f n | J is unimodal. In particular, f n maps the boundary of J into itself. This restriction of f n to J METRIC ATTR...

Ngày tải lên: 14/02/2014, 17:20

... MÔN HỌC KHAI THÁC DỮ LIỆU VÀ ỨNG DỤNG ĐỀ TÀI : MÃ HOÁ HỆ ĐA CẤP ĐA KẾ THỪA THAY CHO PHÉP TÍNH LƯỚI DỰA TRÊN TÀI LIỆU : ENCODING MULTIPLE INHERITANCE HIERARCHIES FOR LATTICE OPERATIONS ... bằng chứng của sự chính xác, m ột loạt bổ đề hữu ích được trình bày. Bổ đề 1 (Thay thế) )()()()()()( zxzyandyx γ γ γ γ γ γ ⊇ ⇒ ⊇ ⊇ . Chứng minh. Bổ đề sau sự thật là )()( yx γ γ ⊇...

Ngày tải lên: 19/01/2014, 13:20

... comfortable for S. Roughly speaking, then, a comfortably embedded submanifold is like a first- order approximation of the zero section of a vector bundle. INDEX THEOREMS FOR HOLOMORPHIC SELF -MAPS 829 Let ... the classical Leau-Fatou flower theorem for maps tangent to the identity achieved in [A2] was an index theorem for holomorphic self -maps of a complex surface fixing pointwise a...

Ngày tải lên: 14/02/2014, 17:20

... y)dy, Annals of Mathematics Uniform bounds for the bilinear Hilbert transforms, I By Loukas Grafakos and Xiaochun Li UNIFORM BOUNDS FOR THE BILINEAR HILBERT TRANSFORMS, I 907 and    Φ 1,k,l (·)e −2πic(ω 1,k,l )(·)   (x)   ≤ ... supported by the NSF. UNIFORM BOUNDS FOR THE BILINEAR HILBERT TRANSFORMS, I 917 Therefore, we obtain I 13  2 ≤ C2 −ηµ 2 − µ p j |I T |...

Ngày tải lên: 14/02/2014, 17:20

... M. Proof of Theorem 1.3. If g denotes the Riemannian metric for M, let M  denote the Riemannian manifold obtained by changing the Riemannian metric for M to g  = g/A, so that the area of M  is 1. ... ˜ε (1−10δ)a n , for some c = c(δ) < ∞, all sufficiently large n and any x ∈ T 2 . Thus, for all sufficiently large n,anyj and a>0, P x 0 (j ∈A n ) ≤ c ˜ε (1−10δ)a n .(2.27) COVER...

Ngày tải lên: 14/02/2014, 17:20

... +1) BOUNDARY BEHAVIOR FOR GROUPS OF SUBEXPONENTIAL GROWTH 1195 Now  m n=0 ln p (|n| +1) ≥ A 2 m for some positive A 2 and any m large enough. Therefore, 1 − φ(t) ≥ A 3 t|ln(t)| p for 0 <t<1 ... is finite. Then for any ε>0 there exists N such that for any n>N v G,S (n) ≥ exp  n ln 2+ε (n)  . BOUNDARY BEHAVIOR FOR GROUPS OF SUBEXPONENTIAL GROWTH 1197 Corollary 2. For...

Ngày tải lên: 14/02/2014, 17:20

... (4.1)] for a statement of Meyer’s formula in the case where D is fundamental; the general case can be derived from equation (18) in §5 of [CS] for example.) It follows that Proposition 3.2 holds for ... ×  τ  t r dlog α, for all r, s, t ∈ Γξ,(50) ×  τ 1  s r dlog α ÷×  τ 2  s r dlog α = ×  τ 1 τ 2  s r dlog α, for all τ 1 ,τ 2 ∈H p ,(51) ×  γτ  γs γr dlog α = ×  τ  s r d...

Ngày tải lên: 16/02/2014, 05:20

... G. ´ Swia¸tek , Decay of geometry for unimodal maps: Negative Schwarzian case, Ann. of Math. 161 (2005), 613–677. [4] ——— , Metric attractors for smooth unimodal maps, Ann. of Math. 159 (2004), ... approach to Milnor’s attractor problem for smooth unimodal maps with critical order not greater than 2. 1. Introduction The dynamical properties of unimodal interval maps...

Ngày tải lên: 16/02/2014, 05:20

... us to handle sequences for which h(p) is signifi- cantly larger than 1 for many primes. Therefore we will, from now on, restrict ourselves to the case when 0 ≤ h(n) ≤ 1 for all n. Suppose that ... log z) 1 In fact, for z ≥ 200. AN UNCERTAINTY PRINCIPLE FOR ARITHMETIC SEQUENCES 613 and the claim follows. For small p<101 3 , set K = [log z/(2 log p)] and observe that for k ≤ K t...

Ngày tải lên: 16/02/2014, 06:20

... ∈ [0, 1] is strictly positive for every J ∈J and almost every x ∈ ∆, and depends continuously on J for almost 646 ARTUR AVILA AND GIOVANNI FORNI every x. Thus, for every δ>0 and J ∈J, there ... · w R p /Z p < for all k ≤ n, and let W s δ (x)=∩W s δ,n (x). lemma 3.4. There exists δ>0 such that for all J ∈J and for almost every x ∈ ∆, J ∩ W s δ (x)=∅. Proof. For any δ<...

Ngày tải lên: 16/02/2014, 06:20