Đề tài " Finite energy foliations of tight three-spheres and Hamiltonian dynamics " potx

... Finite energy foliations of tight three-spheres and Hamiltonian dynamics By H. Hofer, K. Wysocki, and E. Zehnder* FINITE ENERGY FOLIATIONS 143 Proof. Denote by Γ − j the set of negative ... ≥ 0 Annals of Mathematics, 157 (2003), 125–257 Finite energy foliations of tight three-spheres and Hamiltonian dynamics By H. Hofer, K. Wysocki, an...

Ngày tải lên: 05/03/2014, 23:20

... is of index three in Γ k . Proof. It is well known [9] that Γ θ is of index three in SL(2, ) and SL(2, )= 2  j=0 Γ θ  0 −1 11  j . By virtue of the group isomorphism employed in the proof of ... measure of G k . This theorem is a special case of Shah’s more general Theorem 1.4 in [27] on the equidistribution of translates of unipotent orbits. Because of the simple struc...

Ngày tải lên: 14/02/2014, 16:20

... 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 ... right-hand side of the analogue of (2.86). The integral on the right-hand side of (3.9) is of order  1/2 log(1/). Hence we get C 5/6 log(1/) for the second term on the ri...

Ngày tải lên: 14/02/2014, 17:20

... irreducible components of |C n | and of |C ∞ | respecting the genera. Proof. By the definition of the cycle topology, for n  0 each component of C ∞ deforms to parts of some component of C n . This sets ... from the set of irreducible components of C ∞ to the set of irreducible components of C n . The claim on semi-continuity of m follows once we show that the sum of...

Ngày tải lên: 16/02/2014, 05:20

... estimates of H related to the surfaces S t,u and null hypersurfaces C u . • L q (S t,u ) estimates for ∂H and Ric(H). • Energy estimates on C u . • Statement of the estimate for the derivatives of Ric 44 (H). (3) ... the bootstrap assumptions and the results of Sections 6 and 7 we provide a detailed proof of the Asymptotics Theorem. ROUGH EINSTEIN METRICS 1209 6. Bootstrap...

Ngày tải lên: 16/02/2014, 05:20

... multidegree of X equals the sum of multidegrees of components of Y that happen also to be compo- nents of X. By hypothesis, the multidegrees of X and Y coincide, so the sum of multidegrees of the ... schemes of I  and J have equal multidegrees, then I  = J. Proof. Let X and Y be the schemes defined by I  and J, respectively. The multidegree of k[z]/J equals the s...

Ngày tải lên: 16/02/2014, 05:20

... dimensional U ≤ V and finite dimensional Y ≤ W . (1) The codimension of U ⊥ in W equals the dimension of U , and ⊥ (U ⊥ )=U. (2) The codimension of ⊥ Y in V equals the dimension of Y , and ( ⊥ Y ) ⊥ = ... e j )), for i, j ∈ I, and all entries of the |S| matrices that describe the action of members of S on B. Then S  is a finite subset of K and so lies in a finite subfie...

Ngày tải lên: 16/02/2014, 05:20

... cardinality of E, i.e. the number of irreducible components of double curves in X; • f n : the number of n-faces of G, i.e. the number of E n -points of X, for n  3; • f :=  n  3 f n , the number of ... of G, i.e. the total number of E n -points of X, for all n  3; • r n : the number of open n-faces of G, i.e. the number of R n -points of X, for n  3; • r:=...

Ngày tải lên: 16/02/2014, 06:20

... proof of Theorem 6. Let p and (a k ) k≥−m be as in the statement of this theorem. There exist a parameter w>1 and two sequences (U n ) n≥1 and (V n ) n≥1 of finite words as in the definition of ... to decide whether every element of Q(β) ∩(0, 1) has an eventually periodic β-expansion. 5. Proofs of Theorems 1 to 4 We begin by a short proof of Theorem 2. Proof of Theorem...

Ngày tải lên: 16/02/2014, 06:20

... is an arc b of ∂ 4 so that a push off γ  of a ∪ b lies in Q, misses a and separates the boundary components of Q into two sets of two, say one set is ∂ 1 and ∂ 2 and the other is ∂ 3 and ∂ 4 . ... d(k)=m. Let Q be the union of the pair of pants containing k and the pair of pants that contains the adjacent pair of arcs k 1 and k 2 . Let γ be the curve that the two p...

Ngày tải lên: 16/02/2014, 06:20