Đề tài " Reducibility or nonuniform hyperbolicity for quasiperiodic Schr¨odinger cocycles " ppt

... Reducibility or nonuniform hyperbolicity for quasiperiodic Schr¨odinger cocycles By Artur Avila* and Rapha¨el Krikorian REDUCIBLE OR NONUNIFORMLY HYPERBOLIC SCHR ¨ ODINGER COCYCLES 929 C ∞ close ... exponent for quasiperi- odic operators with analytic potential, J. Statist. Phys. 108 (2002), 1203–1218. Annals of Mathematics, 164 (2006), 911–940 Reducibility...

Ngày tải lên: 22/03/2014, 20:20

... vector fields and diffeomorphisms, Math. Z . 229 (1998), 249–318. BIRKHOFF NORMAL FORM 573 [Ga] G. Gallavotti,Acriterion for integrability for perturbed nonresonant harmonic os- cillators. “Wick ordering” ... simple, formal, normal form. This result goes back to C. E. Delaunay [De] and A. Lindstedt [Li] (also see [Po], [Si2]). Nowadays this normal form is named after Birkhoff. The Birkhoff no...

Ngày tải lên: 14/03/2014, 22:20

... dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources By C. Bonatti, L. J. D´ıaz, and E. R. Pujals* A C 1 -GENERIC DICHOTOMY FOR DIFFEOMORPHISMS ... C 1 -generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources By C. Bonatti, L. J. D ´ ıaz, and E. R. Pujals* ARicardo Ma˜n´e (1948–1...

Ngày tải lên: 28/03/2014, 22:20

... By Corollary 2.14, if σ ∈ Sing X (Λ), then σ is Lorenz-like either for X or −X.Ifσ is Lorenz-like for X we have that W ss X (σ) ∩ Λ={σ} by Lemma 2.16-(1) applied to Y = X.Ifσ is Lorenz-like for ... that for any x ∈ Λ X (U), DX T 0 /E s x  < 1 2 . Proof. For each x ∈ Λ X (U) there is t x such that DX t x /E s x  < 1/3. Hence, for each x there is a neighborhood B(x) such...

Ngày tải lên: 28/03/2014, 22:20

... slow dimension growth condition for AH algebras (and therefore, a fortiori for ASH algebras), one obtains counterexamples to the Elliott conjecture of a particularly forceful nature, so that slow ... author would like to thank Mikael Rørdam both for suggesting the search for the automorphisms of Theorem 1.2 and for several helpful discussions, Søren Eilers and Copenhagen University...

Ngày tải lên: 16/02/2014, 06:20

... set {Y ∈ M : τ(Y ) ≤ τ (X)} has the form (∗). Since this is true for every X ∈ M, in fact all of M must have the form (∗). 3. The fundamental theorem 3.1. Theorem. For 0 < α < 1, there exist ... of r for 0 < r <  τ(X) −a. 1508 BRIAN WHITE Slightly weaker statements are true for flows-with-edge that are proper in other open sets U and for which |v(M, ·) − H(M, ·)| is boun...

Ngày tải lên: 06/03/2014, 08:21

... e j ] f ,(20) for all compact open subsets of ˜ G ∞ of the form σU j with σ ∈ ˜ G ∞ . The distribution relation for ˜ν f is ensured by the fact that f is an eigenform for the U p operator with eigenvalue ... the Eichler order of level N + in the quaternion algebra B. As before, to the form φ 0 is associated a unique function f 0 : B × \ ˆ B × / ˆ R × 0 −→ C(11) satisfying T  f = a  f...

Ngày tải lên: 06/03/2014, 08:21

... [15] for information on the Mapping Reflection Principle. For basic forcing technology, the reader is referred to [11] and [14]. Part III of Jech’s [11] gives a good exposition on the combinatorics ... for Scientific Research (C)(2)15540120, Japanese Society for the Promotion of Science. 670 JUSTIN TATCH MOORE Theorem 1.1 (PFA, [3]). If two sets of reals are ℵ 1 -dense, 1 then they are...

Ngày tải lên: 06/03/2014, 08:21

... ∂ j u = Q(t, x, u; du) , for a different Q of the same form, and by combining terms we may assume that g 0j = 0 for j =0. This means that the coefficients of the Lorentzian form ·, · g are given ... h for which a solution exists to the value h = 1. We do this by establishing uniform bounds on the u h in the norm of L 2 t C δ x ; this in turn implies uniform bounds on u h in the Sobolev...

Ngày tải lên: 15/03/2014, 09:20

... H 0 (y)=P for all y in a neighborhood of x. Consequently, H  (y)=P in a neighborhood of x, for all  ≥ 1, proving (3). For the induction step, fix k ≥ 0, and assume the lemma holds for that k. We ... H 2k+2 (y) < dim H 2k+1 (y) for y arbitrarily near x.(9) Then, since we are assuming Lemma 2.2 for k, we must have dim H 2k+1 (y) < dim P−k for all y as in (9), and therefore...

Ngày tải lên: 15/03/2014, 09:20