Tài liệu Đề tài " Statistical properties of unimodal maps: the quadratic family " pptx

... big, lim n→∞ ln(r n (τ n )) ln(c −1 n−1 ) =1.(6.25) Annals of Mathematics Statistical properties of unimodal maps: the quadratic family By Artur Avila and Carlos Gustavo Moreira STATISTICAL PROPERTIES IN THE QUADRATIC FAMILY 861 Recall ... ∈ Ξ i (C d i ) ∩F κ then Ξ i (C d i )=J i+1 [g]. We will concentrate on the analysis of the regularity of Ξ...

Ngày tải lên: 16/02/2014, 05:20

... a t 1 . The proof is then completed by applying the estimates in the proof of Theorem 8.1 and the Markov property. The details are left to the reader. The upper bound for the Hausdorff dimension ... process of growth of a set K t . The evolution of the set over time is described through the normal- ized conformal map g t = g t (z) from the complement of K t ....

Ngày tải lên: 16/02/2014, 05:20

... fixed point of f, and let ˆq be the other preimage of q. The principal nest is the sequence of nested neighborhoods of the critical point I 0 ⊃ I 1 ⊃ I 2 ⊃ I 3 ⊃···, where I 0 =(q, ˆq), and I n+1 is the ... earlier in Section 3.1 of [9] (under the name of “tangent extension”) and in Section 12.2 of [13]. We note that these proofs of the starting condition make ela...

Ngày tải lên: 16/02/2014, 05:20

... estimating the number of solutions of systems of diophantine equations. The almost-everywhere result then follows from a variant of the Borel-Cantelli argument. For further related examples of sequences ... small, the claim is proved. 8.4. Proof of the main theorem. 8.4.1. Due to the linearity in h of the integrals in 8.1, we may assume without loss of generality...

Ngày tải lên: 14/02/2014, 16:20

... from Theorem 1 and Corollary 4; see the discussion after the proof of Theorem 3. 2. Polar curves, affine Lefschetz theory and degree of gradient maps The use of the local polar varieties in the ... Hamm in [H]. In the case of Theorem 1, the homotopy-type claim is a direct consequence of [H, Th. 5], the new part being the relation between the number of n-cells and...

Ngày tải lên: 14/02/2014, 16:20

... if z ∈ Ay and then the branching indices of y,z for f  are the same. On the other hand, the branching index of y for f  is the product of the branching index of y for f times the one of f(y) for ... to exchange the roles of C  1 ,C  2 if the genera g 1 ,g 2 are equal). Therefore we conclude in this case that the conjugate of the surface S  belongs to...

Ngày tải lên: 14/02/2014, 16:20

... show that the restriction of φ is separately continuous in the · 2 -norm, then the result will follow from Proposition 4.3. By fixing all but one of the variables, we reduce to the case of a normal ... k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We...

Ngày tải lên: 14/02/2014, 17:20

... q)=1} area(Σ) . R 2R 2/Q α Figure 2. The parallelogram Σ(α, R, Q). The proof of Theorem 2 relies on the following fact: Theorem 3. Let Spec(α) be the sequence of heights formed by the convergents of α. There exist constants ... namely the square of a holomorphic 1-form. The ergodic theory of the billiards Q λ was first studied by Veech [V1] in the context of 2 sk...

Ngày tải lên: 14/02/2014, 17:20

... by considering the first entry map into the central domain of F. Let δ  i be the domain of the first entry map into the central domain of F which contains δ i . Since the nesting of the central domain ... under the hypotheses of Proposition 2 except for the special form of the central branch. This problem is taken care of by an elementary calculation. Proof o...

Ngày tải lên: 14/02/2014, 17:20

... yields the claim in (2.80). This completes the proof of Lemma 6. This completes the proof of Proposition 4 and hence of Theorem 1. 3. Proof of Theorem 2 In this section we indicate how the arguments ... second term on the right-hand side of the analogue of (2.93). 4. Proof of Theorem 3 In Sections 4–6 we prove Theorems 3–5. The proof follows the same line of re...

Ngày tải lên: 14/02/2014, 17:20