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On dynamics of asymptotically AdS spaces

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The anti-de Sitter (AdS) space is of great interest in contemporary

theoretical physics due to the AdS/CFT correspondence. However, the

question of stability of AdS space is unanswered till now. After

giving the motivation for studies of asymptotically AdS spaces, I will

review dynamics of such spacetimes in the context of AdS instability

problem. This survey will include: evidence for instability of AdS

space, existence and properties of time-periodic solutions, and

finally an application of analytical technique called multiscale or

resonant approximation approach. If time permits, I will comment on

other asymptotically AdS solutions. Along with the results, I will

highlight some details of methods relevant to the topic.