... π
γ
(X, α)=X. The hyperbolic length function descends to the function
: M
γ
g,n
→ R
+
Annals of Mathematics
Growth of the number of
simple closed geodesics on
hyperbolic surfaces
By ... growth of s
X
(L), the number of simple closed
geodesics of length ≤ L on a complete hyperbolic surface X of finite area.
We also study the freq...
... called
essentially non-(n, γ) -simple.
Let us return to the strategy of the proof of Theorem 1.3.9. At the n-th
stage of the induction over the period we consider the family of polynomial
perturbations {
˜
f
ε
<2n
}
ε
<2n
∈HB
N
<2n
(
r)
of ... implies that the number of periodic points is bounded
by an exponential function of the period. The not...
... data:
(i) the intervals (I
k
)
0≤k≤N/n
1
,
(ii) the restriction of C to the union of the I
k
s,
(iii) the values of C outside the I
k
s.
Let us count in each case the number of possibilities:
(i) There ... as (3.1.3) or (3.1.4), we
see functions on M as functions on the cotangent bundle, depending only on the
position. In other words, when we consider the...
... respectively, the conversion of carbon, the initial carbon content in the raw
mixture and the carbon remaining after the composting. Nakasaki et al. (1998a) reported that the
conversion of carbon during ... carbon during the composting process could be calculated based on the ratio of carbon loss
as CO
2
to the carbon contained in the DF alone. In our investiga...
... bounds on the
number of Galois extensions of Q with bounded discriminant. In combination
with the lower bound in Theorem 1.1 for the total number of extensions, this
yields the fact that “most number ... precisely,
EXTENSIONS OF A NUMBER FIELD
737
one may count Galois S
3
-extensions by controlling the 3-class numbers of the
quadratic subextensions; this can be...
... both of these methods, the estimate of the number of sources is that value of
N
s
which minimizes
the criterion. In [9] there is a more thorough discussion concerning determining the number of
degrees ... Decision Theoretic Approaches
The methods that we term decision theoreticapproaches all relyonthe statistical theory of hypothesis
testing to determine the num...
... 2002)
Annals of Mathematics
Hausdorff dimension of the set
of nonergodic directions
By Yitwah Cheung
Annals of Mathematics, 158 (2003), 661–678
Hausdorff dimension of the set
of nonergodic ... Roth’s theorem every algebraic integer satisfies the hypothesis of Theorem 1.
Some generalizations of Theorem 1 are mentioned in Section 2. For the
class of Veec...
... 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 reasoning as in [3, §5], but there ... 1.(2.93)
Substitution into (2.82) 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....
... the exit boundary is nontrivial.
Remark 4. In Lemma 4.2 we used only that the action satisfies the
weak condition (∗). For Lemma 4.3 the assumption that the action satisfies
the strong condition ... follows from (3) of Proposition 1.
6. Applications to growth of groups
Theorem 2. Let G act on (0, 1] by LN maps and let the action satisfy
the strong condition (∗). Assume t...