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4.3 Lyapunov Exponent – The Chaos Hypertextbook

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The Lyapunov exponent is a number that measures stability. In this page, the Lyapunov exponent is applied to an equation that jumps between stability and instability, between chaos and order — the logistic equation.

4.3 Lyapunov Exponent Standard map orbits rendered with Std Map . Descriptions of the sort given at the end of the prevous page are unnatural and clumsy. It would be nice to have a simple measure that could discriminate among the types of orbits in the same manner as the parameters of the harmonic oscillator. Consider two points in a space, X 0 and X 0 + Δx 0 , each of which will generate an orbit in that space using some equation or system of equations. These orbits can be thought of as parametric functions of a variable that is something like time. If we use one of the orbits a referen

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