Abstract
This paper derives an alternative approach to the Melnikov method, which greatly reduces the amount of algebra involved in higher-order calculations. To illustrate this, a particular system is studied for which such a higher-order analysis is necessary, due to an identically vanishing first-order Melnikov function. The results of a second-order calculation imply the existence of transverse homoclinic orbits and, consequently, the existence of a horseshoe.
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