向量丛动力系统研究註记(Ⅱ)──部份1

廖山涛

向量丛动力系统研究註记(Ⅱ)──部份1

廖山涛

北京大学数学系北京 100871

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出版历程
- 收稿日期: 1995-09-18
- 刊出日期: 1996-09-15

Notes on a Study of Vector Bundle Dynamical Systems(Ⅱ)──Part1

Liao Shantao

Mathemoties Department, Peking University, Beijing 100871, P. R. China

摘要

摘要: 过去,向量丛线性动力系统的整体线性性质研究已经显得相当广泛。现在,我们提议研究这种线性系统的扰动性质。我们要考虑的这种扰动系统将不再是线性的,但要研究的性质一般仍是整体性的。再者我们感兴趣的为非一致双曲性。在本文中我们给出了这种扰动的恰当的定义。它虽表现得有几分不太通常,然而它较深地植根于有关微分动力系统理论的典泛方程组中。这里一般的问题是要观察,当扰动发生后,原给系统的何种性质得以保持下来。本文的全部内容是要建立这种类型的一个定理。
- 向量丛 /
- 非一致双曲性 /
- 遍历性 /
- 可容许扰动 /
- 点式有界
Abstract: The study of linear and global.properties of linear dynamical systems on vector bundles appeared rather extensive already in the past.Presently we propose to study perturbations of this linear dynamics The perturbed dynamical system which we shallconsider is no longer linear.while the properties to be studied will be still global in general.Moreover.we are interested in the nonuniformly hyperbolic properties.In this paper,we set an appropriate definition for such perturbations.Though it appears somewhat not quite usual yet has deeper root in standard systens of differential equations in the theory of differentiable dynamical systens The general problen is to see which property of the original given by the dynamical system is persistent when a perturbation takes place.The whole contenl of the paper is deyoted to establishing a theorem of this sort.
- vector bundle dynamics /
- nonuniform hyperbolicity /
- ergodicity /
- admissible perturbation /
- pointwise boundedness

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参考文献(13)

[1]	V.I.Oseledec,A multiplicative ergodic theorem,Lyapunov characteristic numbers for dynamical systems,Trudv Mosk.Mar.Obsce.,19(1969),179-210.
[2]	R.J.Sacker and G.R.Sell,A spectral theory for linear differential systems,J.Differential Eguations,27(1978),320-358.
[3]	R.A.Johnson,K.J.Palmer and G.R.Sell,Ergoic properties of linear dynamical systems,SIAM J.Math..4nal.,18(1987),1-33.
[4]	S.T.Liao,On characteristic exponents construction of a new Borel set for the multiplicative ergodic theorem for vector fields,Acta Scientiarum Naturalium universitatis Pekinensis,29(1993),277-302.
[5]	J.Palis and W.Melo,Geometric Theory of Dynamical Systems,Springer-Verlag,(1982).
[6]	廖山涛,典范方程组,数学学报,17(1974),100-109;175-196;270-295
[7]	廖山涛,向量丛动力系统研究往记(I).应用数学和力学,16(9)(1995),757-766
[8]	Ya.Pesin,Characteristic Lyapunov exonents and smooth ergodic theory,Uspehi Mat.Nauk,32(1977),55-112.
[9]	C.Pugh and M.Shub,Ergedic Attractors,Trans.AMS.,312(1989),1-54.
[10]	C.Pugh,The C^1+x in Pesin theory,Publ.Math.IHES,59(1984),43-161.
[11]	H.Fedrer,Geometric aleasure Theory,Springer-Verlag(1969).
[12]	V.Nemyskii and V.Stepunov,Qualitative Theory of Differential Equations,Princeton University Press(1960).
[13]	P.Wallets,An Introduction to Ergodic Theory,Springer-Verlag(1982).