共查询到20条相似文献,搜索用时 639 毫秒
1.
Nancy Guelman 《Bulletin of the Brazilian Mathematical Society》2002,33(1):75-97
We prove that if 𝒻1 is the time one map of a transitive and codimension one Anosov flow φ and it is C
1-approximated by Axiom A diffeomorphisms satisfying a property called P, then the flow is topologically conjugated to the suspension of a codimension one Anosov diffeomorphism. A diffeomorphism
𝒻 satisfies property P if for every periodic point in M the number of periodic points in a fundamental domain of its central manifold is constant.
Received: 15 March 2001 相似文献
2.
A. A. Gura 《Mathematical Notes》1975,18(1):605-610
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
3.
We show stable ergodicity of a class of conservative diffeomorphisms ofT
n
which do not have any hyperbolic invariant subbundle. Moreover, the uniqueness of SRB (Sinai-Ruelle-Bowen) measure for non-conservativeC
1 perturbations of such diffeomorphisms is verified. This class strictly contains non-partially hyperbolic robustly transitive
diffeomorphisms constructed by Bonatti-Viana [4] and so we answer the question posed there on the stable ergodicity of such
systems. 相似文献
4.
We show that partially hyperbolic diffeomorphisms of \(d\) -dimensional tori isotopic to an Anosov diffeomorphism, where the isotopy is contained in the set of partially hyperbolic diffeomorphisms, are dynamically coherent. Moreover, we show a global stability result, i.e. every partially hyperbolic diffeomorphism as above is leaf-conjugate to the linear one. As a consequence, we obtain intrinsic ergodicity and measure equivalence for partially hyperbolic diffeomorphisms with one-dimensional center direction that are isotopic to Anosov diffeomorphisms through such a path. 相似文献
5.
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
6.
We prove a C1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C1-generic diffeomorphisms. For instance, C1-generic conservative diffeomorphisms are transitive. To cite this article: C. Bonatti, S. Crovisier, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
7.
The only known examples of Anosov diffeomorphisms are hyperbolic automorphisms of infranilmanifolds, and the existence of such automorphisms is a really strong condition on the rational nilpotent Lie algebra determined by the lattice, so called an Anosov Lie algebra. We prove that n⊕?⊕n (s times, s≥2) has an Anosov rational form for any graded real nilpotent Lie algebra n having a rational form. We also obtain some obstructions for the types of nilpotent Lie algebras allowed, and use the fact that the eigenvalues of the automorphism are algebraic integers (even units) to show that the types (5,3) and (3,3,2) are not possible for Anosov Lie algebras. 相似文献
8.
This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting. 相似文献
9.
Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n=3 then either , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of . If n=4 then Π1(M) contains a copy of , provided that the diffeomorphism is not Anosov. To cite this article: J. Rodriguez Hertz et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 321–323. 相似文献
10.
We give a new proof of the existence of compact surfaces embedded in ?3 with Anosov geodesic flows. This proof starts with a noncompact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov. 相似文献
11.
Brownian motions above the group G of volume preserving diffeomorphisms of the torus Td, d?2, are constructed. The asymptotic behaviour for large time of those processes shows the nonexistence of a probability measure invariant under the deterministic incompressible fluid dynamics. The energy induces on the group of volume preserving diffeomorphisms of T2 a Riemannian structure which has a positive renormalized Ricci tensor. 相似文献
12.
Rufus Bowen 《Israel Journal of Mathematics》1975,21(2-3):95-100
It is shown that smooth partitions are weak Bernoulli forC
2 measure preserving Anosov diffeomorphisms. A related type of coding is defined and an invariant discussed.
Supported by the Sloan Foundation and NSF GP-14519. 相似文献
13.
David Fried 《Commentarii Mathematici Helvetici》1982,57(1):237-259
We analyze the dynamics of diffeomorphisms in terms of their suspension flows. For many Axion A diffeomorphisms we find simplest
representatives in their flow equivalence class and so reduce flow equivalence to conjugacy. The zeta functions of maps in
a flow equivalence class are correlated with a zeta function ζ
H
for their suspended flow. This zeta function is defined for any flow with only finitely many closed orbits in each homology
class, and is proven rational for Axiom A flows. The flow equivalence of Anosov diffeomorphisms is used to relate the spectrum
of the induced map on first homology to the existence of fixed points. For Morse-Smale maps, we extend a result of Asimov
on the geometric index.
Partially supported by MCS 76-08795. 相似文献
14.
B. Schmidt 《Geometric And Functional Analysis》2006,16(5):1139-1156
We study the ergodic and rigidity properties of weakly hyperbolic actions. First, we establish ergodicity for C2 volume preserving weakly hyperbolic group actions on closed manifolds. For the integral action generated by a single Anosov
diffeomorphism this theorem is classical and originally due to Anosov.
Motivated by the Franks/Manning classification of Anosov diffeomorphisms on tori, we restrict our attention to weakly hyperbolic
actions on the torus. When the acting group is a lattice subgroup of a semisimple Lie group with no compact factors and all
(almost) simple factors of real rank at least two, we show that weak hyperbolicity in the original action implies weak hyperbolicity
for the induced action on the fundamental group. As a corollary, we obtain that any such action on the torus is continuously
semiconjugate to the affine action coming from the fundamental group via a map unique in the homotopy class of the identity.
Under the additional assumption that some partially hyperbolic group element has quasi-isometrically embedded lifts of unstable
leaves to the universal cover, we obtain a conjugacy, resulting in a continuous classification for these actions.
Partially funded by VIGRE grant DMS-9977371
Received: January 2005 Revision: August 2005 Accepted: September 2005 相似文献
15.
W. Malfait 《Monatshefte für Mathematik》2001,133(2):157-162
We show that from dimension six onwards (but not in lower dimensions), there are in each dimension flat manifolds with first
Betti number equal to zero admitting Anosov diffeomorphisms. On the other hand, it is known that no flat manifolds with first
Betti number equal to one support Anosov diffeomorphisms. For each integer k > 1 however, we prove that there is an n-dimensional flat manifold M with first Betti number equal to k carrying an Anosov diffeomorphism if and only if M is a k-torus or n is greater than or equal to k + 2.
(Received 5 October 2000; in revised form 9 March 2001) 相似文献
16.
In this paper, we define robust transitivity for actions of ℝ2 on closed connected orientable manifolds. We prove that if the ambient manifold is three dimensional and the dense orbit
of a robustly transitive action is not planar, then the action is defined by an Anosov flow, i.e. its orbits coincide with
the orbits of an Anosov flow. 相似文献
17.
Marco Brunella 《Bulletin of the Brazilian Mathematical Society》1993,24(1):89-104
We show that any expansive flow on a 3-manifold which is a Seifert fibration or a torus bundle overS
1 is topologically equivalent to a transitive Anosov flow. This is achieved by analyzing the trace of the stable foliation (with singularities) of the flow on incompressible tori embedded in such a manifold. 相似文献
18.
Yong Fang 《Comptes Rendus Mathematique》2003,336(5):419-422
We show that for a smooth Anosov flow on a closed five dimensional manifold, if it has C∞ Anosov splitting and preserves a C∞ pseudo-Riemannian metric, then up to a special time change and finite covers, it is C∞ flow equivalent either to the suspension of a symplectic hyperbolic automorphism of , or to the geodesic flow on a three dimensional hyperbolic manifold. To cite this article: Y. Fang, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
19.
Let X be a C~1 vector field on a compact boundaryless Riemannian manifold M(dim M≥2),and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = E~sX E~u with E~s uniformly contracting and E~u uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov. 相似文献
20.
Bryna Kra 《Israel Journal of Mathematics》1996,93(1):303-316
For a single aperiodic, orientation preserving diffeomorphism on the circle, all known local results on the differentiability
of the conjugating map are also known to be global results. We show that this does not hold for commutative groups of diffeomorphisms.
Given a set of rotation numbers, we construct commuting diffeomorphisms inC
2-ε for all ε>0 with these rotation numbers that are not conjugate to rotations. On the other hand, we prove that for a commutative
subgroupF ⊂C
1+β, 0<β<1, containing diffeomorphisms that are perturbations of rotations, a conjugating maph exists as long as the rotation numbers of this subset jointly satisfy a Diophantine condition. 相似文献