2024

Dynamical Systems

Name: Dynamical Systems
Code: MAT14360M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area: Mathematics

Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial

Presentation

Many phenomena present irregular behavior. In dynamical systems simple models are studied allowing the analysis of such phenomena, using techniques from Combinatorics, Algebra, Topology, Probability and Statistics. In particular, symbolic dynamics, is a structural concept in the UC.

Sustainable Development Goals

Learning Goals

- Acquire techniques and methods that are structuring of dynamical systems, in particular low-dimensional discrete dynamical systems.
- Develop the ability to apply the techniques acquired in different contexts in other areas of mathematics, but also in natural and human sciences.

Contents

- Interval maps and circle maps: hiperbolicity, symbolic dynamics,
topological conjugation, theorem of Sharkovsky, structural stability, bifurcation, topological invariants,renormalization, chaos, kneading theory of Milnor and Thurston. Combinatorial methods.
- Iteration of complex functions: periodic points and orbits, Julia sets, Mandelbrot set.
Applications.

Teaching Methods

Teaching: Structured exposition, resolution of exercises relating the basic concepts and technical aspects, examples and autonomous study of models focused on applications.
Assessment: Exercises during the period (the final grade is the average of the grades) or final exam.

Teaching Staff

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