... 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...
... 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...
... 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...
... 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...
... 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 <...
... 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...
... 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...
... 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...
... 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...
... 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...