2019 - 2020 | |||||||||||||||||||||||||||||
0321-4858 | Dynamical Systems and Chaos | ||||||||||||||||||||||||||||
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FACULTY OF EXACT SCIENCES | |||||||||||||||||||||||||||||
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Dynamical Systems: Linear systems, fixed points, stability, bifurcations, limit cycles. Nonlinear oscillators, perturbation theory. 3D dynamics, Lorentz model and an introduction to chaotic dynamics. Lyapunov exponents. Discrete maps. Fractals.
Hamiltonian Chaos: Review of analytical mechanics, Liouville theorem, Hamilton-Jacoby equations, integrability. Canonical perturbation theory, resonances and invariant tori, KAM theorem. Transition to chaos, chaotic dynamics, ergodicity and mixing.Kolmogorov-Sinai entropy, chaotic diffusion.