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1.
In this paper we prescribe a fourth order conformal invariant (the Paneitz curvature) on the n-spheres, with n∊{5,6}. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational
problem, we prove some existence results.
Mathematics Subject Classifications (2000): 35J60, 53C21, 58J05, 35J30. 相似文献
2.
Let I be an interval in the real line ℝ. Among the real polynomials that take I to I, we ask which ones do not commute with any increasing bijection of I other than identity. For this purely algebraic problem, the solution involves concepts in topological dynamics. Our main
characterizations are in terms of full orbits of critical points and periodic points. Using these, we obtain simpler criterion,
namely, that for no nontrivial subinterval K⊂I, the successive images {f
n
(K):n=0,1,2,…} form a pairwise disjoint collection. This problem is of interest in topological dynamics because it is about characterization
of polynomials with unique self-topological-conjugacy. 相似文献
3.
T. V. Budnyts’ka 《Ukrainian Mathematical Journal》2009,61(1):164-170
We consider affine mappings from ℝ
n
into ℝ
n
, n ≥ 1. We prove a theorem on the topological conjugacy of an affine mapping that has at least one fixed point to the corresponding
linear mapping. We give a classification, up to topological conjugacy, for affine mappings from R into R and also for affine
mappings from ℝ
n
into ℝ
n
, n > 1, having at least one fixed point and the nonperiodic linear part.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 134–139, January, 2009. 相似文献
4.
Willem Veys 《manuscripta mathematica》1995,87(1):435-448
Tof ∈ℂ[x
1…,x
n
] one associates thetopological zeta function which is an invariant of (the germ of)f at 0, defined in terms of an embedded resolution of (the germ of)f
−1{0} inf
−1{0}. By definition the topological zeta function is a rational function in one variable, and it is related to Igusa’s local
zeta function. A major problem is the study of its poles.
In this paper we exactly determine all poles of the topological zeta function forn=2 and anyf ∈ℂ[x
1,x
2]. In particular there exists at most one pole of order two, and in this case it is the pole closest to the origin. Our proofs
rely on a new geometrical result which makes the embedded resolution graph of the germ off into an ‘ordered tree’ with respect to the so-callednumerical data of the resolution.
The author is a Postdoctoral Fellow of the Belgian National Fund for Scientific Research
N.F.W.O. 相似文献
5.
6.
Sérgio Alvarez Lev Birbrair João Carlos Ferreira Costa Alexandre Fernandes 《Central European Journal of Mathematics》2010,8(2):338-345
We study the topological K-equivalence of function-germs (ℝ
n
, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence
classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs. 相似文献
7.
O. D. Frolkina 《Moscow University Mathematics Bulletin》2009,64(6):253-258
In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions ℝ → ℝ.
In particular, he proved that there exists a continuous function ℝ → ℝ which in some sense “interpolates” all sequences (x
n
)
n∈ℤ ∈ [0, 1]ℤ “simultaneously.” In 2005, M.R. Naulin and C. Uzcátegui unified and generalized Benyamini’s results. In this paper, the case
of topological spaces X and Y with an Abelian group acting on X is considered. A similar problem of “simultaneous interpolation” of all “generalized sequences” using continuous mappings
X → Y is posed. Further generalizations of Naulin-Uncátegui theorems, in particular, multidimensional analogues of Benyamini’s
results are obtained. 相似文献
8.
In this paper we introduce a new type of difference operator Δ
m
n
for fixed m, n ∈ ℕ. We define the sequence spaces ℓ∞(Δ
m
n
), c(Δ
m
n
) and c
0(Δ
m
n
) and study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces.
These notions generalize many earlier existing notions on difference sequence spaces.
相似文献
9.
Carles Casacuberta José Luis Rodríguez Luis Javier Hernández Paricio 《Israel Journal of Mathematics》1998,107(1):301-318
Given an integern>1 and any setP of positive integers, one can assign to each topological spaceX a homotopy universal mapX
(P,n)
→X whereX
(P,n)
is an (n−1)-connected CW-complex whose homotopy groups areP-torsion. We analyze this construction and its properties by means of a suitable closed model category structure on the pointed
category of topological spaces.
The authors acknowledge financial aid given by the DGICYT under projects PB93-0581-C02-01 and PB94-0725. 相似文献
10.
A local variational relation and applications 总被引:3,自引:0,他引:3
In [BGH] the authors show that for a given topological dynamical system (X,T) and an open coveru there is an invariant measure μ such that infh
μ(T,ℙ)≥h
top(T,U) where infimum is taken over all partitions finer thanu. We prove in this paper that if μ is an invariant measure andh
μ(T,ℙ) > 0 for each ℙ finer thanu, then infh
μ(T,ℙ > 0 andh
top(T,U) > 0. The results are applied to study the topological analogue of the Kolmogorov system in ergodic theory, namely uniform
positive entropy (u.p.e.) of ordern (n≥2) or u.p.e. of all orders. We show that for eachn≥2 the set of all topological entropyn-tuples is the union of the set of entropyn-tuples for an invariant measure over all invariant measures. Characterizations of positive entropy, u.p.e. of ordern and u.p.e. of all orders are obtained.
We could answer several open questions concerning the nature of u.p.e. and c.p.e.. Particularly, we show that u.p.e. of ordern does not imply u.p.e. of ordern+1 for eachn≥2. Applying the methods and results obtained in the paper, we show that u.p.e. (of order 2) system is weakly disjoint from
all transitive systems, and the product of u.p.e. of ordern (resp. of all orders) systems is again u.p.e. of ordern (resp. of all orders).
Project supported by one hundred talents plan and 973 plan. 相似文献
11.
We consider a class of hyperbolic 3-orbifoldsO(α/β); the underlying topological space of such an orbifold is the 3-sphere and the singular set is obtained by adding the two
standard (upper and lower) unknotting tunnels to a 2-bridge linkL(α/β) (and associating branching order two to both unknotting tunnels). These 3-orbifolds are extremal with respect to the notion
of Heegaard genus or Heegaard number of 3-orbifolds; it is to be expected that they are also extremal with respect to the
volume, that is the smallest volume hyperbolic 3-orbifolds should belong to this or some closely related class. We show that
an orbifoldO(α/β) has a uniqueD
2-covering by an orbifoldℒ
n(α/β) wose space is the 3-sphere and whose singular set is the same 2-bridge linkL(α/β) used for the construction ofO(α/β); moreoverO(α/β) is hyperbolic if and only ifℒ
n(α/β) is hyperbolic. As the volumes of the orbifoldsℒ
n(α/β) are known resp. can be computed, this allows to compute the volumes of the orbifoldsO(α/β). The problem of computation of volumes remains open for some closely related classes of 3-orbifolds which are also extremal
with respect to the Heegaard genus (for example associating a branching order bigger than two to one or both unknotting tunnels). 相似文献
12.
13.
L. G. Kurakin 《Regular and Chaotic Dynamics》2010,15(1):40-58
The paper is devoted to the analysis of stability of the stationary rotation of a system of n identical point vortices located at the vertices of a regular n-gon of radius R
0 inside a circular domain of radius R. Havelock stated (1931) that the corresponding linearized system has exponentially growing solutions for n ⩾ 7 and in the case 2 ⩽ n ≤ 6 — only if the parameter p = R
02/R
2 is greater than a certain critical value: p
*n
< p < 1. In the present paper the problem of nonlinear stability is studied for all other cases 0 < p ⩽ p
*n
, n = 2, ..., 6. Necessary and sufficient conditions for stability and instability for n ≠ = 5 are formulated. A detailed proof for a vortex triangle is presented. A part of the stability conditions is substantiated
by the fact that the relative Hamiltonian of the system attains a minimum on the trajectory of the stationary motion of the
vortex triangle. The case where the sign of the Hamiltonian is alternating requires a special approach. The analysis uses
results of KAM theory. All resonances up to and including the 4th order occurring here are enumerated and investigated. It
has turned out that one of them leads to instability. 相似文献
14.
S. N. Preobrazhenskii 《Moscow University Mathematics Bulletin》2010,65(4):166-171
It is shown that if a function determined on the segment [−1, 1] has a sufficiently good approximation by partial sums of
its expansion over Legendre polynomial, then, given the function’s Fourier coefficients c
n
for some subset of n ∈ [n
1, n
2], one can approximately recover them for all n ∈ [n
1, n
2]. A new approach to factorization of integer numbers is given as an application. 相似文献
15.
We prove d-linear analogues of the classical restriction and Kakeya conjectures in R
d
. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians, closely
related to heat flow. We conclude by giving some applications to the corresponding variable-coefficient problems and the so-called
“joints” problem, as well as presenting some n-linear analogues for n < d. 相似文献
16.
In this paper, we consider two approaches toward the definition of a topological prime radical of a topological group. In
the first approach, the prime quasi-radical η(G) is defined as the intersection of all closed prime normal subgroups of a topological group G. Its properties are investigated. In the second approach, we consider the set η′(G) of all topologically strictly Engel elements of a topological group G. Its properties are investigated. It is proved that η′(G) is a radical in the class of all topological groups possessing a basis of neighborhoods of the identity element consisting
of normal subgroups.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 15–22, 2004. 相似文献
17.
R. Gabasov N. M. Dmitruk F. M. Kirillova 《Proceedings of the Steklov Institute of Mathematics》2010,271(1):103-124
Let f be an orientation-preserving Morse-Smale diffeomorphism of an n-dimensional (n ≥ 3) closed orientable manifold M
n
. We show the possibility of representing the dynamics of f in a “source-sink” form. The roles of the “source” and “sink” are played by invariant closed sets one of which, A
f
, is an attractor, and the other, R
f
, is a repeller. Such a representation reveals new topological invariants that describe the embedding (possibly, wild) of
stable and unstable manifolds of saddle periodic points in the ambient manifold. These invariants have allowed us to obtain
a classification of substantial classes of Morse-Smale diffeomorphisms on 3-manifolds. In this paper, for any n ≥ 3, we describe the topological structure of the sets A
f
and R
f
and of the space of orbits that belong to the set M
n
\ (A
f
∪ R
f
). 相似文献
18.
Dan Halperin 《Discrete and Computational Geometry》1994,11(1):1-33
We obtain near-quadratic upper bounds on the maximum combinatorial complexity of a single cell in certain arrangements ofn surfaces in 3-space where the lower bound for this quantity is Ω(n
2) or slightly larger. We prove a theorem that identifies a collection of topological and combinatorial conditions for a set
of surface patches in space, which make the complexity of a single cell in an arrangement induced by these surface patches
near-quadratic. We apply this result to arrangements related to motion-planning problems of two types of robot systems with
three degrees of freedom and also to a special type of arrangements of triangles in space. The complexity of the entire arrangement
in each case that we study can be Θ(n
3) in the worst case, and our single-cell bounds are of the formO(n
2
α(n)), O(n
2
logn), orO(n
2
α(n)logn). The only previously known similar bounds are for the considerably simpler arrangements of planes or of spheres in space,
where the bounds are Θ(n) and Θ(n
2), respectively. For some of the arrangements that we study we derive near-quadratic-time algorithms to compute a single cell.
A preliminary version of this paper has appeared inProc. 7th ACM Symposium on Computational Geometry, North Conway, NH, 1991, pp. 314–323. 相似文献
19.
Cvetan Jardas Josip Peari Nikola Sarapa 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):481-492
In this paper we study the problem of convergence in the weak and the vague topology of the sequence
where μ and ν are probability measures on locally compact commutative semigroupS andA
n
=[a
ij
(n)
(i, j, n ɛ N) are double stochastic matrices satisfying some additional conditions. Our results generalize the results in [9]. Theorem
1 also holds if we make some changes on the topological assumptions onS, i.e. if we suppose thatS is a polish space. 相似文献
20.
Seth Pettie† 《Combinatorica》2006,26(2):207-230
Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST(G). A celebrated result of Komlós shows that this problem can be solved with a linear number of comparisons. Somewhat unexpectedly,
MST verification turns out to be useful in actually computing minimum spanning trees from scratch. It is this application
that has led some to wonder whether a more flexible version of MST verification could be used to derive a faster deterministic
minimum spanning tree algorithm. In this paper we consider the online MST verification problem in which we are given a sequence of queries of the form “Is e in the MST of T ∪{e}?”, where the tree T is fixed. We prove that there are no linear-time solutions to the online MST verification problem, and in particular, that
answering m queries requires Ω(mα(m,n)) time, where α(m,n) is the inverse-Ackermann function and n is the size of the tree. On the other hand, we show that if the weights of T are permuted randomly there is a simple data structure that preprocesses the tree in expected linear time and answers queries
in constant time.
* A preliminary version of this paper appeared in the proceedings of the 43rd IEEE Symposium on Foundations of Computer Science
(FOCS 2002), pages 155–163.
† This work was supported by Texas Advanced Research Program Grant 003658-0029-1999, NSF Grant CCR-9988160, and an MCD Graduate
Fellowship. 相似文献