Mechanisms of emergence of complex behavior in systems under nonequilibrium constraints.  Homoclinic bifurcations, theory of
normal forms, spatio-temporal chaos.  Hamiltonian dynamical systems and symplectic methods.  Oscillations, periodic-orbit theory, and
Pollicott-Ruelle resonances. Characterization of chaos and complexity (Lyapunov exponents, fractal dimensions, Kolmogorov-Sinai
dynamical entropy, (epsilon,tau)-entropy per unit time, block entropy).  Probabilistic description by Liouvillian and
Frobenius-Perron operators.  Large-deviation properties and the statistics of extreme events.  Dynamics on networks.