General information 
Course unit name: Dynamic Systems
Course unit code: 568178
Academic year: 20182019
Coordinator: Ernest Fontich Julia
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture 
30 

 Lecture with practical component 
30 
Supervised project 
20 
Independent learning 
70 
Recommendations 

Competences to be gained during study 

Learning objectives 
Referring to knowledge

Teaching blocks 
1. One dimensional and complex dynamics
1.1. Introduction to dynamical systems, discrete and continuous. Basic terminology. Conjugacies.
1.2. Dynamical systems in real dimension 1. Introduction and examples. Bifurcations. Bimodal maps: the quadratic family. Circle homeomorphisms.
1.3. 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.
2. Ndimensional dynamics
2.1. Lyapunov stability.
2.2. Local theory: Hartman’s Theorem, Sternberg’s Theorem and invariant manifolds.
2.3. Normal forms and bifurcations.
2.4. Hyperbolic dynamics.
Teaching methods and general organization 

Official assessment of learning outcomes 
Examinationbased assessment
