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arXiv · 1607.07302

Melnikov's method in String Theory

Yuhma Asano·Hideki Kyono·Kentaroh Yoshida
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Abstract

Melnikov's method is an analytical way to show the existence of classical chaos generated by a Smale horseshoe. It is a powerful technique, though its applicability is somewhat limited. In this paper, we present a solution of type IIB supergravity to which Melnikov's method is applicable. This is a brane-wave type deformation of the AdS$_5\times$S$^5$ background. By employing two reduction ans\"atze, we study two types of coupled pendulum-oscillator systems. Then the Melnikov function is computed for each of the systems by following the standard way of Holmes and Marsden and the existence of chaos is shown analytically.

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Yuhma Asano, Hideki Kyono, Kentaroh Yoshida. 2016-07-25. Melnikov's method in String Theory. https://doi.org/10.1007/jhep09(2016)103

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