Examples of Lyapunov Exponents in Two-Dimensional Systems
In this paper, we construct two examples of two-dimensional dynamical systems. In both examples, we have computed the Lyapunov exponents for the forward trajectory of (0, 0). In the first, such a forward trajectory has positive Lyapunov exponent but does not have sensitive dependence on initial conditions, while the second example has negative Lyapunov exponent but sensitive dependence on initial conditions.
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