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1.
The goal of this paper is to study ergodic and rigidity properties of smooth actions of the discrete Heisenberg group \(\mathcal{H}\). We establish the decomposition of the tangent space of any C∞ compact Riemannian manifold M for Lyapunov exponents, and show that all Lyapunov exponents for the central elements are zero. We obtain that if an \(\mathcal{H}\) action contains an Anosov element, then under certain conditions on the eigenvalues of this element, the action of each central element is of finite order. In particular, there is no faithful codimension one Anosov Heisenberg group action on any compact manifold, and there is no faithful codimension two Anosov Heisenberg group action on tori. In addition, we show smooth local rigidity for higher rank ergodic \(\mathcal{H}\) actions by toral automorphisms, using a generalization of the KAM (Kolmogorov–Arnold–Moser) iterative scheme. 相似文献
2.
Let {Si} be an iterated function system (IFS) on ?d with attractor K. Let (Σ, σ) denote the one‐sided full shift over the alphabet {1, …, ??}. We define the projection entropy function hπ on the space of invariant measures on Σ associated with the coding map π : Σ → K and develop some basic ergodic properties about it. This concept turns out to be crucial in the study of dimensional properties of invariant measures on K. We show that for any conformal IFS (respectively, the direct product of finitely many conformal IFSs), without any separation condition, the projection of an ergodic measure under π is always exactly dimensional and its Hausdorff dimension can be represented as the ratio of its projection entropy to its Lyapunov exponent (respectively, the linear combination of projection entropies associated with several coding maps). Furthermore, for any conformal IFS and certain affine IFSs, we prove a variational principle between the Hausdorff dimension of the attractors and that of projections of ergodic measures. © 2008 Wiley Periodicals, Inc. 相似文献
3.
Zhenjun Yang Huyi Zhang Jimei Min Lingtai Ma Lihe Zhang 《Helvetica chimica acta》1999,82(11):2037-2043
Novel oligonucleotide analogues built from isonucleosides were synthesized by the phosphoramidite approach on an automated DNA synthesizer. The phosphoramidite building blocks were synthesized by phosphitylation of the corresponding protected isonucleosides. The oligonucleotide analogues C – G containing the isonucleoside 1 – 3 were studied with respect to their hybridization properties and enzymatic stability. The oligomers bearing an isonucleoside at the end of the strands all proved stable towards snake-venom phosphodiesterase, but only the oligomers D – G exhibit acceptable duplex stability when hybridized with complementary d(A14). 相似文献
4.
Science China Mathematics - A diffeomorphism f : M → M is pointwise partially hyperbolic on an open invariant subset N ? M if there is an invariant decomposition TNM = Eu ⊕ Ec... 相似文献
5.
Huyi Hu 《Transactions of the American Mathematical Society》2008,360(4):2153-2190
We consider one-sided subshifts with some potential functions which satisfy the Hölder condition everywhere except at a fixed point and its preimages. We prove that the systems have conformal measures and invariant measures absolutely continuous with respect to , where may be finite or infinite. We show that the systems are exact, and are weak Gibbs measures and equilibriums for . We also discuss uniqueness of equilibriums and phase transition.
These results can be applied to some expanding dynamical systems with an indifferent fixed point.
6.
Xianghe Peng Bin Chen Xiang Chen Jun Wang Huyi Wang 《Acta Mechanica Solida Sinica》2012,25(3):285-298
A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys (SMAs). It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka’s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelasticity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results. 相似文献
7.
Huyi Hu 《Communications in Mathematical Physics》1998,191(2):397-407
We consider an expanding map defined on an open region of the plane and study the box dimensions of its invariant sets. Under
the condition that the map leaves invariant a “strong unstable foliation”, we prove that the box dimension of an invariant set is given by δF+δT, where δT is its dimension transverse to and δF is the root of a certain function involving topological pressure.
Received: 6 November 1996 / Accepted: 16 May 1997 相似文献
8.
A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents
We show that there exists a C ∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset ${\mathcal{G}}$ of not full volume and has zero Lyapunov exponent on the complement of ${\mathcal{G}}$ . 相似文献
9.
Huyi Hu 《Communications in Mathematical Physics》1996,176(2):307-320
We consider a compact invariant set of an expanding map of a manifoldM and give upper and lowerbounds for the Hausdorff Dimension dim
H
(), and box dimensionsdim
B
() and dim
B
(). These bounds are given in terms of the topological entropy, topological pressure, and uniform Lyapunov exponents of the map.A measure-theoretic version of these results is also included.Part of this work was done when I was in the Department of Mathematics, University of Arizona. 相似文献
10.
Huyi Hu 《Transactions of the American Mathematical Society》2000,352(5):2331-2367
A diffeomorphism of a compact manifold is called ``almost Anosov' if it is uniformly hyperbolic away from a finite set of points. We show that under some nondegeneracy condition, every almost Anosov diffeomorphism admits an invariant measure that has absolutely continuous conditional measures on unstable manifolds. The measure is either finite or infinite, and is called SBR measure or infinite SBR measure respectively. Therefore, tends to either an SBR measure or for almost every with respect to Lebesgue measure. ( is the Dirac measure at .) For each case, we give sufficient conditions by using coefficients of the third order terms in the Taylor expansion of at .