Lyapounov exponent

In this connection let us remark that in spite of several efforts, the relation between Lyapounov exponents, correlations decay, diffusive and transport properties is still not completely clear. For example a model has been presented (Casati Prosen, 2000) which has zero Lyapounov exponent and yet it exhibits unbounded Gaussian diffusive behavior. Since diffusive behavior is at the root of normal heat transport then the above result (Casati Prosen, 2000) constitutes a strong suggestion that normal heat conduction can take place even without the strong requirement of exponential instability. 

Lyapounov exponents came Within the unit cycle s frame. 

Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A., 1986, Determining Lyapounov exponents from a time series. Physica D (submitted). 

The classical expression for the striation thickness evolution vith time, 5 = 5oexp(—Tit), where Ti is the Lyapounov exponent, shows that f and n values are related to Ti. 

Likewise, the value of the proportionality factor a and the Lyapounov exponent (which can be shown to be proportional to the mean velocity gradient [22]) may change along the flow. 

This almost trivial conclusion may, however, become invalid if the kinetics of a more complex reaction are no longer governed by a set of linear ordinary differential equations. Such a case is, for example, given by the CO oxidation reaction at a Pt(llO) single crystal surface where for certain sets of control parameters (p02, pCO, T) and by operation in a flow system the kinetics may become oscillatory or even chaotic, lliis is illustrated by Fig. 4 which shows the variation of the work function (which is a measure for the O-coverage as well as for the reaction rate) as a function of time for three slightly differing sets of control parameters [15]. le this quantity varies periodically with time in a), it is chaotic in b) and even more in c). The latter data reflect in fact a case of hyperchaos, in which Lyapounov exponents are positive. 

Eckmann, J.P., RueUe, D. Fundamental limitations for estimating dimensions and lyapounov exponents in dynamical systems. Physica D 56, 185-187 (1992)... 

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