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1.
Let f:M~d→M~d(d≥2) be a diffeomorphism on a compact C~∞ manifold on M.If a diffeomorphism f belongs to the C~1-interior of the set of all diffeomorphisms having the barycenter property,then f is Ω-stable.Moreover,if a generic diffeomorphism f has the barycenter property,then f is Ω-stable.We also apply our results to volume preserving diffeomorphisms.  相似文献   

2.
Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL 2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.  相似文献   

3.
Christian Bonatti 《Topology》2005,44(3):475-508
The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T2, perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T3. In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve.  相似文献   

4.
In this paper we show that the incompressible Euler equation on the Sobolev space $H^s(\mathbb{R}^n), s › n ⁄ 2+1$, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesic equation is real analytic. The dynamics in Lagrangian coordinates is described on the group of volume preserving diffeomorphisms, which is an analytic submanifold of the whole diffeomorphism group. Furthermore it is shown that a Sobolev class vector field integrates to a curve on the diffeomorphism group.  相似文献   

5.
We prove that on open manifolds of bounded geometry satisfying a certain spectral condition the component of the identity D infw,0 supr of form preserving diffeomorphisms is a submanifold of the identity component of all bounded Sobolev diffeomorphisms. D infw,0 supr inherits a natural Riemannian geometry and we can solve Euler equations in this context.Research supported by NSF grant # DMS-9303215 and Emory-Greifswald Exchange Program  相似文献   

6.
We generalize the prequantization central extension of a group of diffeomorphisms preserving a closed 2-form ω, to an abelian extension of a group of diffeomorphisms preserving a closed vector valued 2-form ω up to a linear isomorphism (ω-equivariant diffeomorphisms). Every abelian extension of a simply connected Lie group can be obtained as the pull-back of such a prequantization abelian extension.  相似文献   

7.
Let Ω be a symmetric cone and V the corresponding simple Euclidean Jordan algebra. In our previous papers (some with G. Zhang) we considered the family of generalized Laguerre functions on Ω that generalize the classical Laguerre functions on R+. This family forms an orthogonal basis for the subspace of L-invariant functions in L2(Ω,dμν), where dμν is a certain measure on the cone and where L is the group of linear transformations on V that leave the cone Ω invariant and fix the identity in Ω. The space L2(Ω,dμν) supports a highest weight representation of the group G of holomorphic diffeomorphisms that act on the tube domain T(Ω)=Ω+iV. In this article we give an explicit formula for the action of the Lie algebra of G and via this action determine second order differential operators which give differential recursion relations for the generalized Laguerre functions generalizing the classical creation, preservation, and annihilation relations for the Laguerre functions on R+.  相似文献   

8.
There exists a diffeomorphism on the n-dimensional torus Tn which is conjugate with a hyperbolic linear automorphism, but is not an Anosov diffeomorphism. A diffeomorphismf: Tn→Tn has such a property iff is separating and belongs to the C0 closure of the Anosov diffeomorphisms.  相似文献   

9.
We construct homogeneous quasi-morphisms on the identity component of the group of area preserving diffeomorphisms of the two dimensional torus, whose restriction to the subgroup of diffeomorphisms with support in any fixed disc equals Calabi's invariant. To cite this article: P. Py, C. R. Acad. Sci. Paris, Ser. I 343 (2006).  相似文献   

10.
We show that closed orientable smooth four-manifolds with non-trivial volume flux group and fundamental group of subexponential growth type are finitely covered by a manifold homeomorphic to S3×S1, S2×T2 or a nil-manifold. We also show that if a compact complex surface has non-trivial volume flux group then it has zero minimal volume.  相似文献   

11.
Let Diff(S 1) be the group of orientation preserving C ?∞? diffeomorphisms of S 1. In 1999, P. Malliavin and then in 2002, S. Fang constructed a canonical Brownian motion associated with the H 3/2 metric on the Lie algebra diff(S 1). The canonical Brownian motion they constructed lives in the group Homeo(S 1) of Hölderian homeomorphisms of S 1, which is larger than the group Diff(S 1). In this paper, we present another way to construct a Brownian motion that lives in the group Diff(S 1), rather than in the larger group Homeo(S 1).  相似文献   

12.
Given measure preserving transformationsT 1,T 2,...,T s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref 1,f 2,...,f s ?L (X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL 2-norm is ∫ x f 1 dμ·∫ x f 2 dμ...∫ x f s dμ for anyf 1,f 2...,f s ?L (X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.  相似文献   

13.
We consider mappings of the m-dimensional torus Tm (m ≥ 2) that are C 1-perturbations of linear hyperbolic automorphisms. We obtain sufficient conditions for such mappings to be one-to-one hyperbolic mappings (i.e., Anosov diffeomorphisms). These results are used to study the blue-sky catastrophe related to the vanishing of a saddle-node invariant torus with a quasiperiodic winding in a system of ordinary differential equations.  相似文献   

14.
For any non-uniform lattice Γ in SL2(?), we describe the limit distribution of orthogonal translates of a divergent geodesic in Γ\SL2(?). As an application, for a quadratic form Q of signature (2, 1), a lattice Γ in its isometry group, and v 0 ∈ ?3 with Q(v 0) > 0, we compute the asymptotic (with a logarithmic error term) of the number of points in a discrete orbit v 0Γ of norm at most T, when the stabilizer of v 0 in Γ is finite. Our result in particular implies that for any non-zero integer d, the smoothed count for the number of integral binary quadratic forms with discriminant d 2 and with coefficients bounded by T is asymptotic to c · T log T + O(T).  相似文献   

15.
We prove that every homomorphism from a discrete Kazhdan group to the group of orientation-preserving diffeomorphisms of the circle of class C1+α (α>1/2) has a finite image.  相似文献   

16.
In this paper, we study the quasi-neutral limit of compressible Euler-Poisson equations in plasma physics in the torus Td. For well prepared initial data the convergence of solutions of compressible Euler-Poisson equations to the solutions of incompressible Euler equations is justified rigorously by an elaborate energy methods based on studies on an λ-weighted Lyapunov-type functional. One main ingredient of establishing uniformly a priori estimates with respect to λ is to use the curl-div decomposition of the gradient.  相似文献   

17.
Let M be an m-dimensional differentiable manifold with a nontrivial circle action S={St}tR, St+1=St, preserving a smooth volume μ. For any Liouville number α we construct a sequence of area-preserving diffeomorphisms Hn such that the sequence converges to a smooth weak mixing diffeomorphism of M. The method is a quantitative version of the approximation by conjugations construction introduced in [Trans. Moscow Math. Soc. 23 (1970) 1].For m=2 and M equal to the unit disc D2={x2+y2?1} or the closed annulus A=T×[0,1] this result proves the following dichotomy: αR?Q is Diophantine if and only if there is no ergodic diffeomorphism of M whose rotation number on the boundary equals α (on at least one of the boundaries in the case of A). One part of the dichotomy follows from our constructions, the other is an unpublished result of Michael Herman asserting that if α is Diophantine, then any area preserving diffeomorphism with rotation number α on the boundary (on at least one of the boundaries in the case of A) displays smooth invariant curves arbitrarily close to the boundary which clearly precludes ergodicity or even topological transitivity.  相似文献   

18.
By an (abstract) Kummer variety Kd we mean the d-dimensiona1 torus Td modulo the involution ? ? — ?. The 2d elements in Td of order two are fixed points of the involution and therefore Kd has 2d isolated singularities (for d ≧ 3). Any simplicial decomposition of Kd must have at least as many vertices. In this paper we describe a highly symmetrical simplicial decomposition of Kd with 2d vertices such that the link of each vertex is a combinatorial real projective space ?Pd-1 with 2d—1 vertices. The automorphism group of order (d + 1)! 2d admits a natural representation in the affine group of dimension d over the field with two elements. A particular case is the classical Kummer surface with 16 nodes (d=4). In this case our 16-vertex triangulation has a close relationship with the abstract Kummer configuration 166.  相似文献   

19.
Inverses and regularity of band preserving operators   总被引:1,自引:0,他引:1  
The following four main results are proved here. Theorem 3.3.For each one-to-one band preserving operatorT:XXon a vector lattice its inverseT−1:T(X) → Xis also band preserving. This answers a long standing open question. The situation is quite different if we move from endomorphisms to more general operators. Theorem 4.2.For a vector lattice X the following two conditions are equivalent:
1.
i)|For each one-to-one band preserving operator T:XXu from X to its universal completion Xu the inverse T−1 is also band preserving.
2.
ii)|For each non-zero x ? X and each non-zero band U ⊂ {x}dd there exists a non-zero semi-component of x in U.
Theorem 5.1.For a vector lattice X the following two conditions are equivalent.
1.
i)|Each band preserving operator T:XXu is regular.
2.
ii)|The d-dimension of X equals 1.
Corollary 5.9.Let X be a vector sublattice of C(K) separating points and containing the constants, where K is a compact Hausdorff space satisfying any one of the following three conditions: K is metrizable, or connected, or locally connected. Then each band preserving operatorT: XXis regular.  相似文献   

20.
It is shown that if G is a finite group of degree preserving automorphisms of R, the ring of n×n generic matrices over a field of characteristic zero generated by d > 1 elements, then the fixed ring RG can never be generated by d elements unless n = 1 and G is a quasireflection group. As a consequence, for n > 1, RG is never a generic matrix ring.  相似文献   

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