The assignment of this subject was based on multiple deliviries. You can find two folders containing the main blocks of the course:
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One dimensional and complex dynamics
- Introduction to dynamical systems, discrete and continuous. Basic terminology. Conjugacies.
- Dynamical systems in real dimension 1. Introduction and examples. Bifurcations. Bimodal maps: the quadratic family. Circle homeomorphisms.
- Dynamical Systems on the complex plane. Riemann surfaces and iteration of holomorphic functions.Normal families: The Fatou and Julia sets. Local theory: periodic points and linearization. Global theory: connected components of the Fatou set. Parameter spaces: the Mandelbrot set and main conjectures.
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N-dimensional dynamics
- Lyapunov stability.
- Local theory: Hartman’s Theorem, Sternberg’s Theorem and invariant manifolds.
- Normal forms and bifurcations.
- Hyperbolic dynamics.
Final Mark 10 (MH)