共查询到20条相似文献,搜索用时 15 毫秒
1.
We shall prove the equivalences of a non-degenerate circle-preserving map and a Möbius transformation in\(\hat {\mathbb{R}}^n \), of a non-degenerate geodesic-preserving map and an isometry in ?n, of a non-degenerate line-preserving map and an affine transformation in ?n. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry. 相似文献
2.
Guowu Yao 《Journal of Mathematical Analysis and Applications》2007,334(2):950-953
Recently, B. Li and Y. Wang proved that if (n?2) is a circle-preserving map, then f is a Möbius transformation if and only if f is a non-degenerate map, where a map f is degenerate if the image is a circle. Furthermore, they conjectured that there should exist no degenerate map, or equivalently, f is a Möbius transformation if and only if f is a circle-preserving map. In this note, we construct a degenerate circle-preserving map to show that the conjecture is not true. 相似文献
3.
史淑国 《数学年刊A辑(中文版)》2004,(3)
将双曲上半空间Hn中的曲面视为Rn中的曲面,导出这两种共形浸入下平均曲率向量的关系;证明了这两种浸入下Gauss映照是一样的;给出Hn中给定Gauss映照的曲面的Weierstrass表示;证明了一个唯一性结果. 相似文献
4.
In this paper we give some conclusions on Newton non-degenerate analytic map germs on Kn (K = ? or ?), using information from their Newton polyhedra. As a consequence, we obtain the exact value of the Lojasiewicz exponent at the origin of Newton non-degenerate analytic map germs. In particular, we establish a connection between Newton non-degenerate ideals and their integral closures, thus leading to a simple proof of a result of Saia. Similar results are also considered to polynomial maps which are Newton non-degenerate at infinity. 相似文献
5.
Naoyuki Koike 《Results in Mathematics》2003,43(1-2):150-155
A non-degenerate equiaffine immersion of codimension one into an equiaffine space is locally expressed in terms of its conormal map and its affine fundamental form. The expression is called the Lelieuvre’s formula. We recently defined the notions of an equiaffine immersion of general codimension and its transversal volume element map. In this paper, we locally express a non-degenerate equiaffine immersion of general codimension into an equiaffine space in terms of its transversal volume element map and its affine fundamental form. 相似文献
6.
关于区间上的Lorenz映射 总被引:1,自引:0,他引:1
本文引进了变换ζ.首先,用比文[4]简捷的方法证明了Lorenz映射的Sarkovski定理并更正了文[4]中的一个错误,还得到了扩张的Lorenz映射中周期点的存在性与其扩张常数之间的关系.其次,证明了Lorenz映射与其在变换ζ的像具有相等的捏制行列式.此外,给出了广义的Lorenz映射的周期点的存在性适合Sarkovski序关系的一个充分条件 相似文献
7.
Hong Jianqiao 《数学年刊B辑(英文版)》1995,16(3):361-370
THEGAUSSMAPOFTIMELIKESURFACESINR_1~n¥HONGJIANQIAOAbstract:Gaussmapsoforientedtimelike2-surfacesinarecharacterized,anditisshown... 相似文献
8.
Lijuan Zhang Xu Zhang Wei Liang 《Journal of Difference Equations and Applications》2013,19(11):1817-1842
In this paper, we study small perturbations of a class of chaotic discrete systems in Banach spaces induced by snap-back repellers. If a map has a regular and non-degenerate snap-back repeller, then it still has a regular and non-degenerate snap-back repeller under a sufficiently small perturbation. Consequently, the perturbed system is still chaotic in the sense of both Devaney and Li–Yorke as the original one. Furthermore, in order to study structural stability of maps with regular and non-degenerate snap-back repellers, we first discuss structural stability of strictly A-coupled-expanding maps in Banach spaces. Applying this result, we show that a map with a regular and non-degenerate snap-back repeller in a Banach space is C 1 structurally stable on its chaotic invariant set. 相似文献
9.
本文利用复射影空间到欧氏空间的第一标准嵌入,对于复射影空间的子流形建立了一种广义的Gauss映照,并给出了这种广义的Gau8s映照是调和映照和相对仿射映照的条件。 相似文献
10.
分数次积分在局部Hardy空间上的有界性质 总被引:1,自引:1,他引:0
证明了当0<αn/(n-α)时,分数次积分Iα是局部Hardy空间hp(Rn)到空间hp(Rn)+Lq(Rn)的一个线性映射. 相似文献
11.
The authors introduce a notion of a weak graph map homotopy (they call it
M-homotopy), discuss its properties and applications. They prove that the weak graph
map homotopy equivalence between graphs coincides with the graph homotopy equivalence
defined by Yau et al in 2001. The difference between them is that the weak graph map
homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over
the graph homotopy transformation. As its applications, they investigate the mapping
class group of a graph and the 1-order MP-homotopy group of a pointed simple graph.
Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is
invariant up to the weak graph map homotopy equivalence. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(4):329-332
The first return map of a C3 unimodal map to a neighbourhood of the critical point is conjugated by a real-analytic diffeomorphism to a map with negative Schwarzian derivative. Consequently, we obtain the classification of the metric attractors for smooth unimodal maps with non-degenerate critical point. 相似文献
13.
Maps are studied, i.e., cell decompositions of closed two-dimensional surfaces, or two-dimensional atoms which encode bifurcations of Liouville fibrations of non-degenerate integrable Hamiltonian systems. Any finite group G is proved to be a symmetry group of an orientable map (of an atom). Moreover, one such map X(G) is constructed algorithmically. Upper bounds are obtained for the minimal genus Mg(G) of an orientable map with the given symmetry group G and for the minimal number of vertices, edges, and sides of such maps. 相似文献
14.
Damjana Kokol Bukovšek 《Linear algebra and its applications》2007,420(1):34-50
We study non-degenerate irreducible homomorphisms from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup of m-by-m matrices over the same field. We prove that every non-degenerate homomorphism from the multiplicative semigroup of all n-by-n matrices to the semigroup of (n + 1)-by-(n + 1) matrices when n ? 3 is reducible and that every non-degenerate homomorphism from the multiplicative semigroup of all 3-by-3 matrices to the semigroup of 5-by-5 matrices is reducible. 相似文献
15.
本文应用 Smith周期变换理论 ,根据球面在周期变换下的指数 ,对球面到光滑流形的连续映射做了进一步探讨 ,从而得到了 Munkholm型定理 . 相似文献
16.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(5):553-558
It was known to Poincaré that a non-degenerate periodic orbit in a Hamiltonian system persists to nearby energy-levels. In this Note, we consider the analogous problem for relative periodic orbits in symmetric Hamiltonian systems. We show that non-degenerate relative periodic orbits also persist when shifting to nearby values of the energy-momentum map, under the hypothesis that the group of symmetries acts freely. 相似文献
17.
18.
This paper gives a generalization of the classical Borel's Lemma. Then as an application of this generalized Borel's Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of Cm into Pn(C) (n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved. 相似文献
19.
Lucas C. F. Ferreira Marcelo Montenegro Matheus C. Santos 《Journal d'Analyse Mathématique》2016,128(1):1-49
We define the Polish space R of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, σ-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on R, showing that it is \({F_\sigma }\) as a subset of R× R and bi-reducible to E0. We also explicitly describe when a non-degenerate rank-1 system is topologically isomorphic to its inverse. 相似文献
20.
Guo Wei YU 《数学学报(英文版)》2022,(1):179-204
For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number,which indicates chaotic dynamics.Our results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus. 相似文献