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1.
In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces. 相似文献
2.
Codimension two bifurcation of a vibro-bounce system 总被引:1,自引:0,他引:1
Guanwei?LuoEmail author Yandong?Chu Yanlong?Zhang Jianhua?Xie 《Acta Mechanica Sinica》2005,21(2):197-206
A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item)) 相似文献
3.
Changrong Zhu Guangping Luo Kunquan Lan 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2010
The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation manifolds, the perturbed system has various coexistence of homoclinic solutions which are linearly independent. 相似文献
4.
V. M. Petrogradsky 《代数通讯》2013,41(3):918-928
We study Lie nilpotent varieties of associative algebras. We explicitly compute the codimension growth for the variety of strong Lie nilpotent associative algebras. The codimension growth is polynomial and found in terms of Stirling numbers of the first kind. To achieve the result we take the free Lie algebra of countable rank L(X), consider its filtration by the lower central series and shift it. Next we apply generating functions of special type to the induced filtration of the universal enveloping algebra U(L(X)) = A(X). 相似文献
5.
We give a construction for Gorenstein ideals of codimension 4 which we believe have maximal graded Betti numbers for their Hilbert function. 相似文献
6.
7.
Mark Andrea A. de Cataldo 《Transactions of the American Mathematical Society》1997,349(6):2359-2370
We prove that there are only finitely many families of codimension two nonsingular subvarieties of quadrics which are not of general type, for and . We prove a similar statement also for the case of higher codimension.
8.
The question of the existence of a proper closed densely defined suboperator whose domain contains a given linear space is answered. Such suboperators with codimension one domains are described. The motivation for studying this topic comes from the theory of extremal extensions of (non-densely defined) positive operators. 相似文献
9.
Dongmei Xiao 《Journal of Dynamics and Differential Equations》2008,20(4):961-980
In this paper we consider a five-parameter family of planar vector fields where μ = (μ
1, μ
2, μ
3, μ
4, μ
5), which is a small parameter vector, and c(0) ≠ 0. The family X
μ
represents the generic unfolding of a class of nilpotent cusp of codimension five. We discuss the local bifurcations of X
μ, which exhibits numerous kinds of bifurcation phenomena including Bogdanov-Takens bifurcations of codimension four in Li
and Rousseau (J. Differ. Eq. 79, 132–167, 1989) and Dumortier and Fiddelaers (In: Global analysis of dynamical systems, 2001), and Bogdanov-Takens bifurcations
of codimension three in Dumortier et al. (Ergodic Theory Dynam. Syst. 7, 375–413, 1987) and Dumortier et al. (Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals,
1991). After making some rescalings, we obtain the truncated systems of X
μ
. For a truncated system, all possible bifurcation sets and related phase portraits are obtained. When the truncated system
is a Hamiltonian system, the bifurcation diagram and the related phase portraits are given too. Hopf bifurcations are studied
for another truncated system. And it shows that the system has the Hopf bifurcations of codimension at most three, and at
most three limit cycles occur in the small neighborhood of the Hopf singularity.
Dedicated to Professor Zhifen Zhang in the occasion of her 80th birthday 相似文献
10.
Briana Foster-Greenwood 《代数通讯》2013,41(10):4350-4365
Reflection length and codimension of fixed point spaces induce partial orders on a complex reflection group. Motivated by connections to the algebraic structure of cohomology governing deformations of skew group algebras, we show that Coxeter groups and the infinite family G(m, 1, n) are the only irreducible complex reflection groups for which reflection length and codimension coincide. We then discuss implications for the degrees of generators of Hochschild cohomology. Along the way, we describe the codimension atoms for the infinite family G(m, p, n), give algorithms using character theory, and determine two-variable Poincaré polynomials recording reflection length and codimension. 相似文献