Topics in Dynamical Systems

Code:

M3018

Acronym:

M3018

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2016/2017 - 2S (of 06-02-2017 to 20-05-2017)

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	12	Official Study Plan	3	-	3	28	81

Teaching language

Portuguese

Objectives

An introduction to the theory of discrete-time and continuous-time dynamical systems.

Learning outcomes and competences

To identify basic properties of dynamical systems.

Working method

Presencial

Program

Discrete systems:
- Basic definitions
- Hyperbolicity
- Quadratic family
- Symbolic Dynamics
- Topological conjugacy
- Chaos
- Structural stability
- Sarkovskii Theorem

Continuous Systems:
- Linear systems
- Stability and bifurcation
- Limite sets
- Poincaré sections
- Poincaré-Bendixson Theorem

Mandatory literature

Devaney Robert L.; An introduction to chaotic dynamical systems. ISBN: 0-201-13046-7

Complementary Bibliography

Hirsch Morris W.; Differential equations, dynamical systems, and introduction to chaos. ISBN: 0-12-349703-5
Elaydi Saber N.; Discrete chaos. ISBN: 1-584-88002-3
Alligood Kathleen T.; Chaos. ISBN: 0-387-94677-2

Teaching methods and learning activities

Blackboard and shalk.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Calculation formula of final grade

The average of two written tests: one on March 23, another one on May 24.