Lyapunov Exponent Calculation

The Lyapunov exponent A(x0) measures the gap of trajectories. Let x0,x0 + e be two close points, then we write the Lyapunov exponent by: eenX(x° = | fn (x0 + e)-f (x0) |. For the limits of e and n, we have

It is pointed out that xi = f (x0) and fn(x0) = f (fn 1 (x0)), consequently dfn(x0)/ dx = f (xn-1) f(xn-2) ■ ■■ f (x1) f (xn-1). ^0) is written

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