向量丛动力系统研究注记(Ⅱ)──部份2

Notes on a study of vector Bundle Dynamical systems(Ⅱ)──Part 2

摘要: 在这部份2中.我们先证明部份1中叙述的定理3.1^[15].这证明是通过换变数的办法,把原方程组化成微分动力系统理论中.有关典范方程组的一种形式来完成的.然后用定理3.1^[15]加上预备定理2.1来证明部份1中宣布的本文主要定理.有关可容许扰动的定义包含在这部份2的附录中.这主要定理的意义描述在部份1引言中.
- 向量丛动力系统 /
- 非一致双曲性 /
- 遍历性 /
- 可容许扰动 /
- 点式有界
Abstract: In the part 2,theorem 3.1 stut ed in part 1^[15] is proved first.The proof is obtained via a way of changing variables to reduce the original system of differentialequations to a form concerning Standard systems of equations in the theory ofdifferentiable dynamical systems.Then by using theorem 3.1 together with thepreliminary theorem 2.l,foe main theorem of this paper announced in part 1 is proved.The definition of admissible perturbation is contained in the appendix of part 2.Themeanings of the main theorem is described in the introduction of part 1.
- vector bundle dynamics /
- nonuniform hyperbolicity /
- ergodicity /
- admissible perturbation /
- pointwise boundedness

[1]	V.I.Oseledec,A multiplicative ergodic theorem,Lyapunov characteristic numbers for dynamical systems,Trudv Mosk.Mat.Obsce.,19(1969),179-210.
[2]	R.J.Sacker and G.R.Sell,A spectral theory for linear differential systems,J.Differential Equations,27(1978),320-358.
[3]	R.A.Johnson,K.J.Palmer and G.R.Sell,Ergoic properties of linear dynamical systems,SIAM J.Math.Anal.,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 Scientiarunt Naturaliunr Universitatis Pekinensis,29(1993),277-320.
[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.
[7]	廖山涛,向量从动力系统研究注记(I),应用数学和力学,16,9(1995),813-823.
[8]	Ya.Pesin,Characteristic Lyapunov exponents and smooth ergodic theory,Uspefti Mat.Nauk,32(1977),55-112.
[9]	C.Pugh and M.Shub,Ergodic Attractors,Trans.AMS.,312(1989),1-54.
[10]	C.Pugh,The C^1+x hypothesis in Pesin theory,Publ.Math.IHES,59(1984),43-161.
[11]	H.Fedrer,Geometric Measure Theory,Springer-Verlag(1969).
[12]	V.Nemyskii and V.Stepunov,Qualirativo Theory of Differential Equations,Princeton University Press(1960).
[13]	P.Wallets,An Introdtrotion to Ergodic Theory,,Springer-Verlag(1982).
[14]	S.Lefschetz,Differential Equationt.:Geometric Theory,Wiley 1963).
[15]	廖山涛,向量丛动力系统研究注记(Ⅱ)—部份,应用数学和力学17(9)(1996),805-818.