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Classification of Special anosov Endomorphisms of Nil-manifolds

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Acta Mathematica Sinica,English Series 2019年第12期35卷 1871-1890页

作者： Seyed Mohsen MOOSAVI Khosro TAJBAKHSH Department of Mathematics Faculty of Mathematical Sciences Tarbiat Modares University

In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to *** f is a spec... 详细信息

关键词： Hyperbolicity anosov endomorphisms special anosov endomorphisms TA maps nilmanifolds

Quasisymmetric property for conjugacies between anosov diffeomorphisms of the two-torus

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Science China Mathematics 2010年第3期53卷 663-670页

作者： HU HuYi 1 & JIANG YunPing 2, 1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA 2 Department of Mathematics, the Graduate Center and Queens College of CUNY, Flushing, NY 11367, USA Department of Mathematics Michigan State University East Lansing USA Department of Mathematics the Graduate Center and Queens College of CUNY Flushing USA

We prove that the restrictions of the conjugacy between two anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.

关键词： quasisymmetry anosov diffeomorphisms conjugacy Hlder condition Markov partition

An equivalent condition for anosov maps with zero entropies

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Chinese Science Bulletin 1996年第11期41卷 887-890页

作者：代雄平 Lingnan College of Zhongshan University Guangzhou 510275 China

Sakai defined the anosov maps on compact metric spaces. Sun proved that anosovmaps have the orbit-topological stability, Markov partitions and ζ-funtions. Aformulation for the topological entropy of an anosov map wes given by Sun in reference. In this note we will also study the topological entropy of an anosov map, but we willpay attention to the relation between the entropy and the number of periodic points. Thefollowing consequenee will be proved.

关键词： anosov map topological entropy Markov partition pseudo-orbits tracing property expansive map.

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anosov映射的ζ函数

科学通报 1990年第16期35卷 1278-1279页

作者：孙文祥河北师范学院数学系石家庄 050091

描述周期点状况的ζ函数,是动力系统研究的重要课题。Manning曾证明了Smale猜测,即公理A微分同胚具有有理ζ函数。之后关于具有有理ζ函数的映射类,张筑生确定了扩张映射,冯庆富推广到公理A自覆盖映射,Hiraide确定了紧度量空间上具有伪... 详细信息

描述周期点状况的ζ函数,是动力系统研究的重要课题。Manning曾证明了Smale猜测,即公理A微分同胚具有有理ζ函数。之后关于具有有理ζ函数的映射类,张筑生确定了扩张映射,冯庆富推广到公理A自覆盖映射,Hiraide确定了紧度量空间上具有伪轨跟踪性质的可扩同胚。本文使用伪轨跟踪

关键词：伪轨跟踪性质 anosov 拓扑稳定性扩张映射

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环面上anosov自映射的π1性质

科学通报 1987年第20期32卷 1526-1529页

作者：章梅荣北京大学数学系

一、引言一个微分动力系统的π1性质是与其结构稳定性和拓扑共轭类密切相关的（见文献[1—3]）。本文利用文献[4,5]中关于结构稳定性的工作,研究了环面上anosov自映射的π1性质,得出了以下结论。定理1 设a:Tm→Tm是m维环面Tm上的双曲... 详细信息

一、引言一个微分动力系统的π1性质是与其结构稳定性和拓扑共轭类密切相关的（见文献[1—3]）。本文利用文献[4,5]中关于结构稳定性的工作,研究了环面上anosov自映射的π1性质,得出了以下结论。定理1 设a:Tm→Tm是m维环面Tm上的双曲自同态,且设a既不是双曲自同构又不是扩张自同态。则对充分C1邻近a的anosov自映射f,f不是π1映射。

关键词：自映射 anosov 自同态环面曲面

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anosov映射的单一化拓扑稳定性

科学通报 1989年第8期34卷 635-635页

作者：孙文祥河北师范学院数学系石家庄

Sakai指出anosov映射在连续满射构成的空间内不具有拓扑稳定性(扩张映射除外),而我们的结果表明anosov映射保持着轨道定向意义下的稳定性,即单一化拓扑稳定性。设M为紧致度量空间,以C~0(M)记M上全体连续满射(带C~0拓扑)形成的空间。对f... 详细信息

Sakai指出anosov映射在连续满射构成的空间内不具有拓扑稳定性(扩张映射除外),而我们的结果表明anosov映射保持着轨道定向意义下的稳定性,即单一化拓扑稳定性。设M为紧致度量空间,以C~0(M)记M上全体连续满射(带C~0拓扑)形成的空间。对f∈C~0(M),记称为f的轨道空间。为

关键词：拓扑稳定性 anosov 满射

The Barycenter Property for Robust and Generic Diffeomorphisms

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Acta Mathematica Sinica,English Series 2016年第8期32卷 975-981页

作者： Manseob LEE Department of Mathematics Mokwon University

Let f ： Md →Md（d 〉 2） be a diffeomorphism on a compact C^∞ manifold on M. If a diffeomorphism f belongs to the Cl-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 12-stable. We also apply our results to volume preserving diffeomorphisms.

关键词： Barycenter property robust generic hyperbolic Axiom A anosov

SHADOWING,EXPANSIVENESS AND SPECIFICATION FOR C^1-CONSERVATIVE SYSTEMS

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Acta Mathematica Scientia 2015年第3期35卷 583-600页

作者： Mario BESSA Manseob LEE 文晓 Universidade da Beira Interior Rua Marques d'Avila e Bolama Department of Mathematics Mokwon University The School of Mathematics and Systems Science Beihang University

We prove that a Cl-generic volume-preserving dynamical system （diffeomor- phism or flow） has the shadowing property or is expansive or has the weak specification property if and only if it is anosov. Finally, as in [10, 27], we prove that the Cl-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system （diffeomorphism or flow） is anosov.

关键词： Shadowing expansiveness specification generic anosov volume-preserving star systems

Diffeomorphisms with the M0-shadowing Property

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1760-1770页

作者： Xu ZHANG Xin Xing WU Department of Mathematics Shandong UniversityWeihai 264209P.R.China School of Sciences Southwest Petroleum UniversityChengdu 610500P.R.China Department of Electronic Engineering City University of Hong KongHong Kong SARP.R.China

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.

关键词： anosov diffeomorphism average shadowing property Mα-shadowing