Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes

Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing resonant approximation that accurately captures a simplified form long-term evolution of small initial data. Topics covered include turbulent regular motion, dynamical recurrences analogous to Fermi-Pasta-Ulam phenomena oscillator chains, relations between nonrelativistic Schrodinger equations harmonic potentials. Special mention given way classical weakly strongly systems illuminated by perturbative considerations within corresponding quantum theories, particular, relation chaos theory.