共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the ergodic theory of non-conservative C
1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose
supports coincide with the homoclinic class. Second, we show that generic (for the weak topology) ergodic measures of C
1-generic diffeomorphisms are non-uniformly hyperbolic: they exhibit no zero Lyapunov exponents. Third, we extend a theorem
by Sigmund on hyperbolic basic sets: every isolated transitive set Λ of any C
1-generic diffeomorphism f exhibits many ergodic hyperbolic measures whose supports coincide with the whole set Λ. 相似文献
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3.
We investigate the properties of a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifold defined by Ismagilov, Losik, and Michor. We provide both vanishing and nonvanishing results and applications to foliated symplectic bundles and to Hamiltonian actions of finitely generated groups. 相似文献
4.
Xiang Zhang 《Journal of Differential Equations》2010,248(7):1603-2298
In this paper we study the problem on embedding germs of smooth diffeomorphisms in flows in higher dimensional spaces. First we prove the existence of embedding vector fields for a local diffeomorphism with its nonlinear term a resonant polynomial. Then using this result and the normal form theory, we obtain a class of local Ck diffeomorphisms for k∈N∪{∞,ω} which admit embedding vector fields with some smoothness. Finally we prove that for any k∈N∪{∞} under the coefficient topology the subset of local Ck diffeomorphisms having an embedding vector field with some smoothness is dense in the set of all local Ck diffeomorphisms. 相似文献
5.
We compute the Hofer distance for a certain class of compactly supported symplectic diffeomorphisms of 2n. They are mainly characterized by the condition that they can be generated by a Hamiltonian flow
H
t
which possesses only constantT-periodic solutions for 0 <T 1. In addition, we show that on this class Hofer's and Viterbo's distances coincide. 相似文献
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In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically,
ifS is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphereS
4n−1 by a torus, and if the second Betti numberb
2(S)≥2 then dimS=7, 11, 15, whereas, ifb
2 (S)≥5 then dimS=7. We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases
not excluded by these bounds.
During the preparation of this work the authors were partially supported by an NSF grant.
This article was processed by the author using the LATEX style file from Springer-Verlag. 相似文献
8.
In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically,
if is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphere S
4
n
-1 by a torus, and if the second Betti number then 7, 11, 15, whereas, if then . We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases
not excluded by these bounds.
Received: 6 January 1997 / Revised version: 11 June 1997 相似文献
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We construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or cyclic isotropy sets. All
such actions are not compatible with any symplectic form on the manifold in question. In order to cover the case of non-symplectic
fixed point sets, we use two smooth 4-manifolds (one symplectic and one non-symplectic) which become diffeomorphic after taking
the products with the 2-sphere. The second type of actions is obtained by constructing smooth circle actions on spheres with
non-symplectic cyclic isotropy sets, which (by the equivariant connected sum construction) we carry over from the spheres
on products of 2-spheres. Moreover, by using the mapping torus construction, we show that periodic diffeomorphisms (isotopic
to symplectomorphisms) of symplectic manifolds can provide examples of smooth fixed point free circle actions on symplectic
manifolds with non-symplectic cyclic isotropy sets. 相似文献
11.
Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse, Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, pp. 191-202; S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9-18; S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études Sci. 50 (1979) 101-151]. It turns out that in the space of Cr smooth diffeomorphisms Diffr(M) of a compact surface M there is an open set U such that a Baire generic diffeomorphism f∈U has infinitely many coexisting sinks. In this paper we make a step towards understanding “how often does a surface diffeomorphism have infinitely many sinks.” Our main result roughly says that with probability one for any positive D a surface diffeomorphism has only finitely many localized sinks either of cyclicity bounded by D or those whose period is relatively large compared to its cyclicity. It verifies a particular case of Palis' Conjecture saying that even though diffeomorphisms with infinitely many coexisting sinks are Baire generic, they have probability zero.One of the key points of the proof is an application of Newton Interpolation Polynomials to study the dynamics initiated in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I, Ann. of Math., in press, 92 pp.; V. Kaloshin, A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II, preprint, 85 pp.]. 相似文献
12.
Javier Ribón 《Journal of Differential Equations》2012,253(12):3211-3231
In [Xiang Zhang, The embedding flows of C∞ hyperbolic diffeomorphisms, J. Differential Equations 250 (5) (2011) 2283-2298] Zhang proved that any local smooth hyperbolic diffeomorphism whose eigenvalues are weakly nonresonant is embedded in the flow of a smooth vector field. We present a new and more conceptual proof of such result using the Jordan-Chevalley decomposition in algebraic groups and the properties of the exponential operator.We characterize the hyperbolic smooth (resp. formal) diffeomorphisms that are embedded in a smooth (resp. formal) flow. We introduce a criterion showing that the presence of weak resonances for a diffeomorphism plus two natural conditions imply that it is not embeddable. This solves a conjecture of Zhang. The criterion is optimal, we provide a method to construct embeddable diffeomorphisms with weak resonances if we remove any of the conditions. 相似文献
13.
Carlo Bianca 《Nonlinear Analysis: Hybrid Systems》2011,5(1):32-51
The highly complex nature of the transport in thermostatted billiards has been of interest in the last few decades because of industrial and medical applications. The onset of hyperbolic dynamics (deterministic chaos) in such a billiard has evidenced an interesting stabilization of the transport properties, especially in microporous media. Recently, different mathematical methods have been developed for establishing hyperbolicity in thermostatted billiards, among these, the Weyl-flow and the conformally symplectic structure techniques.This paper deals with analytical investigations on the possible hyperbolic nature of two thermostatted billiards: The nonequilibrium Ehrenfest gas (NEEG) and the pump model (PM). Despite numerical investigations supporting the idea of their dissipative dynamics, the hyperbolicity of these billiards has not been yet established. The analysis developed in this paper shows how the Weyl-flow technique has failed for NEEG, revealing the necessity to develop new strategies in order to obtain hyperbolicity. On the contrary, we prove that the PM has a conformally symplectic structure, which is the basis for establishing the hyperbolicity of such a hybrid dynamical system. 相似文献
14.
In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori. 相似文献
15.
Chris Macmeikan 《Indagationes Mathematicae》2004,15(2):257-267
Let G be a connected semi-simple algebraic group over . Fix a maximal torus T in G with coordinate ring T. Let Φ+ be the set of positive roots of G with respect to T. The pair (T, A), where A = {kerα}α?φ+, is a toral arrangement. We show that if G is simply connected then the module of A-derivations D(A) is a free T-module. 相似文献
16.
Our aim is to extend existing results about differentiable rigidity of higher rank abelian actions by automorphisms of a torus.
Previous proofs have required an assumption of semisimplicity, that is, that the action is by commuting diagonalizable matrices. Here we introduce a technique that utilizes the unipotent
part of a non-semisimple action, which allows us to discard the semisimplicity assumption. In its place we will make a technical
assumption that the spectrum of the action restricted to leaves of the coarse Lyapunov decomposition is sufficiently narrow. 相似文献
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We prove that if an area-preserving homeomorphism of the torus in the homotopy class of the identity has a rotation set which is a nondegenerate vertical segment containing the origin, then there exists an essential invariant annulus. In particular, some lift to the universal covering has uniformly bounded displacement in the horizontal direction. 相似文献
20.
Wilmer J. Colmená rez Rodriguez 《Transactions of the American Mathematical Society》2005,357(10):4131-4140
In this paper we show nonuniform hyperbolicity for a class of attractors of flows in dimension three. These attractors are partially hyperbolic with central direction being volume expanding, contain dense periodic orbits and hyperbolic singularities of the associated vector field. Classical expanding Lorenz attractors are the main examples in this class.