## Nonlinear dynamics, chaos theory and complex systems

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Units : Physics of Complex Systems and Statistical Mechanics | ULB492

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.

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