Block A:
History of chaos and its importance in natural sciences and engineering; Fundamentals of chaos theory (classification of trajectories, parameter influence, nonlinear systems, Poincaré section); Stability, bifurcation (Lyapunov stability, the interface of stable and unstable regions); Analysis of equilibrium states (equilibrium states of continuous DS, basic types of bifurcations); Periodic solutions of dynamical systems (limit cycles, heteroclinic and homoclinic trajectories)
Block B:
Chaotic dynamical systems (bifurcations in chaotic systems, Lyapunov exponents, frequency spectrum); Chaos in discrete and continuous systems (the shift map, transitivity, chaos in the sense of Devaney and Li-Yorke, Poincaré's theorem); Chaos and fractals (fractal, Mandelbrot and Julius sets, IFS and TEA algorithms); Fractals (self-similarity, fractal dimensions and collage theorem)
Block C:
Quantification and qualification tools of dynamic systems (shadowing lemma); Wolf's and Kantz's algorithm for calculation of Lyapunov exponents (Takens' embedding theorem); 0-1 test for chaos, approximate and sampling entropy
History of chaos and its importance in natural sciences and engineering; Fundamentals of chaos theory (classification of trajectories, parameter influence, nonlinear systems, Poincaré section); Stability, bifurcation (Lyapunov stability, the interface of stable and unstable regions); Analysis of equilibrium states (equilibrium states of continuous DS, basic types of bifurcations); Periodic solutions of dynamical systems (limit cycles, heteroclinic and homoclinic trajectories)
Block B:
Chaotic dynamical systems (bifurcations in chaotic systems, Lyapunov exponents, frequency spectrum); Chaos in discrete and continuous systems (the shift map, transitivity, chaos in the sense of Devaney and Li-Yorke, Poincaré's theorem); Chaos and fractals (fractal, Mandelbrot and Julius sets, IFS and TEA algorithms); Fractals (self-similarity, fractal dimensions and collage theorem)
Block C:
Quantification and qualification tools of dynamic systems (shadowing lemma); Wolf's and Kantz's algorithm for calculation of Lyapunov exponents (Takens' embedding theorem); 0-1 test for chaos, approximate and sampling entropy