Đề tài " Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers " ppt

... Sing Y (Λ Y (U)) is hyperbolic, Annals of Mathematics Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers By C. A. Morales, M. J. Pacifico, ... all C 1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding cen- tral direction, and a...

Ngày tải lên: 28/03/2014, 22:20

... and convergence for a higher order flow in conformal geometry By Simon Brendle 1. Introduction An important problem in conformal geometry is the construction of con- formal metrics for which a certain ... C ≤− 1 C w 2 H 2k + C for all 0 ≤ t ≤ T .Thus, we conclude that w H 2k ≤ C for all 0 ≤ t ≤ T. Therefore, the evolution equation has a solution which is defined for all time. 6. C...

Ngày tải lên: 28/03/2014, 22:20

... only holds for robustly transitive systems. A C 1 -GENERIC DICHOTOMY FOR DIFFEOMORPHISMS 367 Acknowledgments. We thank IMPA (Rio de Janeiro) and the Laboratoire de Topologie (Dijon) for their warm ... of transitive sets (i.e. the general case). Second, proceeding in this way can emphasize the additional difficulties and subtleties of the proof for transitive sets. Proof of The...

Ngày tải lên: 28/03/2014, 22:20

... for suggesting the search for the automorphisms of Theorem 1.2 and for several helpful discussions, Søren Eilers and Copenhagen University for their hospitality in 2003, and George Elliott for ... 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, s...

Ngày tải lên: 16/02/2014, 06:20

... 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 bounded. For ... 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 <...

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

... 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 isomorphic. ... [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...

Ngày tải lên: 06/03/2014, 08:21

... 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 by 1 2  g ij + ... q(u k )(du k ) 2 of the equations for u k are uniformly bounded in the space L 2 ([−T,T]; H s−1 ). Then (WP4) combined with Duhamel’s formula show that du k is uniformly bounded...

Ngày tải lên: 15/03/2014, 09:20

... the condition for the error term in (4.1), and with R 2 (z,w,t) supported in d(z, w)  ι(X, g)/4, t  1 and with x  2ε. (Here, and henceforth, we use (x, y) as local coordinates for the z variable ... xQ j a j−1 . (4.30) Here b j is supported in x ∈ [ε, 2ε] and our initial condition for a j is that it vanish for x>2ε. These are regular singular ODEs for the a j . The first eq...

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 therefor...

Ngày tải lên: 15/03/2014, 09:20