Liao Shantao. Notes on a Study of Vector Bundle Dynamical Systems(Ⅱ)──Part1[J]. Applied Mathematics and Mechanics, 1996, 17(9): 759-771.
Citation: Liao Shantao. Notes on a Study of Vector Bundle Dynamical Systems(Ⅱ)──Part1[J]. Applied Mathematics and Mechanics, 1996, 17(9): 759-771.

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

  • Received Date: 1995-09-18
  • Publish Date: 1996-09-15
  • 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.
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  • [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 C1+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).
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