Probing analytical and numerical integrability: the curious case of (AdS5 × S 5) η

Abstract Motivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background (AdS5 × S 5) η . We start by revisiting conclusions from earlier studies on string motion in (ℝ × S 3) η and (AdS3) η and then move on to more complex problems of (ℝ × S 5) η and (AdS5) η . Discussing both analytically and numerically, we deduce that while (AdS5) η strings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself