Chaotic Dynamics

Course content

Mappings. Time series. Orbits. Periodic orbits. Fixed points and periodic points. Finding periodu points. Eventually periodic points. Families of mappings and bifurcations. Transitivity. Sensitive dependence. Dense periodic points. One-dimensional chaos. Devaney ingredients. The logistic map. Period-three points and chaos. Period-doubling bifurcation, Two-dimensional chaos. The Henon map. The Horseshoe map. Dimensions. Systems of differential equations. Homoclinic chaos. Dynamics on labels, Fractals. Abstract similarity map, Abstract similarity sets, Labeling. Chaos in stochastic processes