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1.
M. Yu. Matviichuk 《Ukrainian Mathematical Journal》2008,60(7):1099-1113
For a mapping f ∈ C
r
(I, I), r ≥ 0, we consider the problem of the existence of a mapping close to it that has periodic trajectories of given periods in
common with f.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 937–948, July, 2008. 相似文献
2.
In this paper we prove that, for anyn≥3, there exist infinitely manyr∈N and for each of them a smooth, connected curveC
r in ℙ
r
such thatC
r lies on exactlyn irreducible components of the Hilbert scheme Hilb(ℙ
r
). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type. 相似文献
3.
A set N ⊂ ℝ
d
is called a weak
ɛ-net (with respect to convex sets) for a finite X ⊂ ℝ
d
if N intersects every convex set C with |X ∩ C| ≥ ɛ|X|. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ ℝ
d
for which every weak 1/r -net has at least Ω(r log
d−1
r) points; this is the first superlinear lower bound for weak ɛ-nets in a fixed dimension. 相似文献
4.
We provide an affirmative answer to the C
r
-Closing Lemma, r ≥ 2, for a large class of flows defined on every closed surface. 相似文献
5.
Yu. N. Bibikov 《Mathematical Notes》1997,61(1):29-37
We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT
m. The flow on the torusT
m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect
to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions
for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 34–44, January, 1997.
Translated by S. K. Lando 相似文献
6.
In this article the dynamics of generic Cr (r ≥ 3) perturbations of complex polynomials are considered. The attention is focused on the determination of the existence
of large or invariant components of the complement of the basin of ∞, where the interesting dynamics occur. 相似文献
7.
For functions with the integrable βth power, where β = (r + 1 + 1/p)−1, we obtain asymptotically exact lower bounds for the approximation by local splines of degreer and defectk ≥r/2 in the metric ofL
p.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 12, pp. 1628–1637, December, 1999. 相似文献
8.
Let Δ3 be the set of functions three times continuously differentiable on [−1, 1] and such that f″′(x) ≥ 0, x ∈ [−1, 1]. We prove that, for any n ∈ ℕ and r ≥ 5, there exists a function f ∈ C
r
[−1, 1] ⋂ Δ3 [−1, 1] such that ∥f
(r)∥
C[−1, 1] ≤ 1 and, for an arbitrary algebraic polynomial P ∈ Δ3 [−1, 1], there exists x such that
| f(x) - P(x) | 3 C?n \uprhonr(x), \left| {f(x) - P(x)} \right| \geq C\sqrt n {{\uprho}}_n^r(x), 相似文献
9.
Sylvie Ruette 《Israel Journal of Mathematics》2002,127(1):253-277
We construct aC
rtransformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy.
Whereas the assumption ofC
∞ ensures existence of maximal measures for an interval map, it shows we cannot weaken the smoothness assumption. We also compute
the local entropy of the example. 相似文献
10.
Chong Qing Cheng 《数学学报(英文版)》2011,27(2):397-404
Given an integrable Hamiltonian h
0 with n-degrees of freedom and a Diophantine frequency ω, then, arbitrarily close to h
0 in the C
r
topology with r < 2n, there exists an analytical Hamiltonian h
ε with no KAM torus of rotation vector ω. In contrast with it, KAM tori exist if perturbations are small in C
r
topology with r > 2n. 相似文献
11.
O. Yu. Teplins’kyi 《Ukrainian Mathematical Journal》2008,60(2):310-326
We prove that any C3+β-smooth diffeomorphism preserving the orientation of a circle with rotation number from the Diophantine class Dδ, 0 < β < δ < 1, is C2+β−δ-smoothly conjugate to a rigid rotation of the circle by a certain angle.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 268–282, February, 2008. 相似文献
12.
Ricardo Mañé 《Bulletin of the Brazilian Mathematical Society》1990,20(2):1-24
Letf be aC
r
diffeomorphism,r≥2, of a two dimensional manifoldM
2, and let Λ be a horseshoe off (i.e. a transitive and isolated hyperbolic set with topological dimension zero). We prove that there exist aC
r
neighborhoodU off and a neighbourhoodU of Λ such that forg∈U, the Hausdorff dimension of ∩
n
g
n
(U) is aC
r−1 function ofg. 相似文献
13.
Aubin Arroyo 《Bulletin of the Brazilian Mathematical Society》2007,38(3):455-465
In the context of Cr-flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity
(in the sense of Smale) for C1-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincaré flow and on the nature
of the singular set) under which a transitive attractor with singularities of a C2-flow on a 3-manifold is singular hyperbolic. 相似文献
14.
O. G. Parfenov 《Journal of Mathematical Sciences》1998,92(1):3630-3634
The Gelfand widths of the unit ball of H2(ν) (the weighted Hardy space) with respect to the metric of the space L∞(Tr) are considered (here Tr is the circle of radius r centered at the origin), as well as the Bernstein widths of the unit ball of H∞ with respect to the metric of the space L2(Tr, μ). Asymptotic formulas for the widths in question are established for arbitrary measures ν, μ. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 134–140.
Translated by S. V. Kislyakov. 相似文献
15.
For a (smooth irreducible) curveC of genus g and Clifford indexc>2 with a linear seriesg
d
r
computing c (so
) it is well known thatc + 2 ≤d ≤2 (c + 2), and if
then 2c + 1 ≤g ≤ 2c + 4 unlessd = 2c + 4 in which caseg = 2c + 5.
Let c ≥ 0 andg be integers. If 2c + 1 ≤g ≤2c + 4 we prove that for any integerd <g such thatd ≡c mod 2 andc + 2 ≤d < 2(c + 2) there exists a curve of genus g and Clifford index c with a gd
r computing c. Ford ≥c + 6 (i.e.r ≥ 3) we construct this curve on a surface of degree 2r-2 in ℙr, and ford ≥c + 8 (i.e.r ≥ 4) we show that such a curve cannot be found on a surface in ℙr of smaller degree. In fact, if gd
r computes the Clifford index c of C such thatc + 8 ≤d ≤ 2c + 3 then the birational morphism defined by this series cannot map C onto a (maybe, singular) curve contained in a surface
of degree at most 2r-3 in ℙr. 相似文献
16.
Shung-Liang Wu 《Graphs and Combinatorics》2002,18(3):687-690
In this paper we investigate the necessary and sufficient conditions for the existence of 3 · 2
r
+1-cycle system of K
n
– C
n
, where C
n
is any Hamilton cycle of K
n
and r ≥ 0.
Received: December 17, 1999 Final version received: July 25, 2000
Present address: 15 Guang Ming 10 St. Sec. 1, Chu-Bei, Hsin-Chu, 302, Taiwan, ROC 相似文献
17.
The behavior of bounded solutions to the equation Δu−c(x)u=0 on riemannian manifolds of special type
A. G. Losev 《Mathematical Notes》1999,65(2):175-180
In the paper we consider solutions of the equation Δu−c(x)u=0,c(x)≥0, on complete Riemannian manifolds constituted as follows: the exterior of some compact set is isometric to the direct product
of the semiaxis by some compact manifold with the metricds
2=h
2(r)dr
2+g
2(r)dθ2. Necessary and sufficient conditions under which bounded solutions of the equation have a limit independent of θ asr→∞ are obtained and also conditions under which the two-sided Liouville theorem is valid.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 215–221, February, 1999. 相似文献
18.
F. Béguin S. Crovisier F. Le Roux 《Bulletin of the Brazilian Mathematical Society》2006,37(2):275-306
In this paper, we study pseudo-rotations of the open annulus, i.e. conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of
the pseudo-rotation). We prove in particular that, for every pseudo-rotation h of angle ρ, the rigid rotation of angle ρ is in the closure of the conjugacy class of h. We also prove that pseudo-rotations are not persistent in Cr topology for any r ≥ 0. 相似文献
19.
Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r * of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1). 相似文献
20.
The multicolor Ramsey number Rr(H) is defined to be the smallest integer n=n(r) with the property that any r-coloring of the edges of the complete graph Kn must result in a monochromatic subgraph of Kn isomorphic to H. It is well known that 2rm<Rr(C2m+1)<2(r+2)!m and Rr(C2m)≥(r−1)(m−1)+1. In this paper, we prove that Rr(C2m)≥2(r−1)(m−1)+2.
This research is supported by NSFC(60373096, 60573022) and SRFDP(20030141003) 相似文献
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