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991.
Consider G=Z
22 as the group generated by two commuting involutions, and let
be a smooth G-action on a smooth and closed manifold M. Suppose that the fixed point set of Φ consists of two connected components, F
n
and F
n-1, with dimensions n and n−1, respectively. In this paper we prove that, if in the fixed data of Φ at least two eigenbundles over F
n
have dimension greater than n, and at least one eigenbundle over F
n-1 has dimension greater than n−1, then the action (M,Φ) bounds equivariantly.It is well known that, if
is a smooth involution on a smooth and closed m-dimensional manifold M
m
such that the fixed point set of T has constant dimension n, and if m > 2n, then (M
m
,T) bounds equivariantly; this fact was proved by R. E. Stong and C. Kosniowski 27 years ago. As a consequence of our result,
we will see that the same fact is true when, besides n-dimensional components, the fixed point set contains additional (n−1)-dimensional components. 相似文献
992.
993.
Boštjan Potočnik Gašper Mušič Borut Zupančič 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(1):41-57
The paper proposes a new translation algorithm that translates a hybrid system described as a discrete hybrid automaton (DHA) into an equivalent piecewise affine (PWA) system. The translation algorithm exploits, among others, a new technique for cell enumeration in hyperplane arrangement, all proposed in this paper. The new translation technique enables the transfer of several analysis and synthesis tools developed for PWA systems to a DHA class of hybrid systems. 相似文献
994.
A certain class of affine delay equations is considered. Two cases for the forcingfunction M are treated: M locally integrable deterministic, and M a random process with stationaryincrements. The Lyapunov spectrum of the homogeneous equation is used to decompose the state spaceinto finite-dimensional and finite-codimensional subspaces. Using a suitable variation of constants representation, formulas for the projection of the trajectories onto the above subspaces are obtained. If the homogeneous equation is hyperbolic and M has stationary increments, existence and uniqueness of a stationary solution for the affine stochastic delay equation is proved. The existence of Lyapunov exponents for the affine equation and their dependence on initial conditions is als studied. 相似文献
995.
Takeshi Yoshimoto 《Journal of Functional Analysis》2009,256(6):1708-1730
Let (Ω,ß,μ) be a finite measure space and let (S,F,ν) be another probability measure space on which a measure preserving transformation φ is given. We introduce the so-called affine systems and prove a vector-valued nonlinear random ergodic theorem for the random affine system determined by a strongly F-measurable family of affine operators, where B is a reflexive Banach space, is a strongly F-measurable family of linear contractions on L1(Ω,B) as well as on L∞(Ω,B) and ξ is a function in (I−T)Lp(S×Ω,B) (1?p<∞) with the operator T defined by Tf(s,ω)=[Tsfφs](ω) which denotes the F⊗ß-measurable version of Tsfφs(ω). Moreover, some variant forms of the nonlinear random ergodic theorem are also obtained with some examples of affine systems for which the nonlinear ergodic theorems fail to hold. 相似文献
996.
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the
complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal
holonomy approach. Indeed, we explain how these submanifolds can be regarded as the unique complex orbits of the (projectivized)
isotropy representation of an irreducible Hermitian symmetric space. Moreover, we show how these important submanifolds are
related to other areas of mathematics and theoretical physics. Finally, we state a conjecture about the normal holonomy group
of a complete and full complex submanifold of the complex projective space.
Research partially supported by GNSAGA (INdAM) and MIUR of Italy. 相似文献
997.
We generalize the quasicrystallographic groups in the sense of Novikov and Veselov from Euclidean spaces to pseudo-Euclidean and affine spaces. We prove that the quasicrystallographic groups on Minkowski spaces whose rotation groups satisfy an additional assumption are projections of crystallographic groups on pseudo-Euclidean spaces. An example shows that the assumption cannot be dropped. We prove that each quasicrystallographic group is a projection of a crystallographic group on an affine space. 相似文献
998.
A sufficient and necessary condition for the existence of a Hamilton cycle in a graph bundle with a cycle as a base and a tree as a fibre is obtained. 相似文献
999.
1000.