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 AdS5×S5 background. By employing two reduction ansätze, 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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Asano, Y., Kyono, H. & Yoshida, K. Melnikov’s method in String Theory. J. High Energ. Phys. 2016, 103 (2016). https://doi.org/10.1007/JHEP09(2016)103
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DOI: https://doi.org/10.1007/JHEP09(2016)103