Code: | M3029 | Acronym: | M3029 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Mathematics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:M | 7 | Official Study Plan | 2 | - | 3 | 28 | 81 |
3 |
The syllabus presents examples and results mainly on low dimensional dynamics in order to emphasize the geometrical, topological and probabilistic methods in this reasearch area and their broad applications in other sciences.
The syllabus is an introduction to a recent but outstanding research mathematical area. The list of topics chosen for this course includes a preliminary classical content and results from recent research, besides several examples and applications.
Analysis, Measure Theory and Topology.
1. Discrete dynamical systems.
Notions: orbit, periodicity, recurrence, wandering points, transitivity, genericity, conjugacy, stability, minimality.
2. Motivation for the study of dynamical systems.
3. Detailed analysis of several examples.
4. Homeomorphisms of the unit circle: Theorems of Poincaré and Denjoy.
5. Sharkowskii order (period 3 implies chaos).
6. Dynamical proofs of some results in Number Theory.
The content of the syllabus is presented in the lectures, where examples, exercises and problems are discussed. Reading suggestions, additional bibliography and other resources are available for students at the FCUP library.
designation | Weight (%) |
---|---|
Exame | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 47,00 |
Frequência das aulas | 28,00 |
Trabalho escrito | 6,00 |
Total: | 81,00 |
There will be no record of absences.
The evaluation consists of a written exam (marks between 0 and 20).
Not applicable.
Not applicable.
According to the FCUP regulations, the students have access to an exam to improve their grades.
Jury: Maria Pires de Carvalho