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Differential Equations and Dynamical Systems

Code 13318
Year 1
Semester S1
ECTS Credits 10
Workload TP(30H)
Scientific area Física e Matemática
Entry requirements None
Learning outcomes To aquire advanced knowledge in dynamical systems and differential equations.
To prepare students for research in theoretical physics and modern mathematical physics.

Syllabus 1. General theory
2. Linear equations
3. Stability and hyperbolicity
4. structural stability
Main Bibliography [Differential Equations: DE; Dynamical Systems: DS]
VI Arnol’d 1992 Ordinary DE 3ed, Springer
L Barreira, C Valls 2010 Equações Diferenciais: Teoria Qualitativa, IST Press
C Bonatti, LJ Díaz, M Viana 2005 Dynamics Beyond Uniform Hyperbolicity, Springer
C Chicone 2006 Ordinary DE with Applications 2ed, Springer
CI Doering, AO Lopes 2016 Equações Diferenciais Ordinárias 6ed, IMPA
J Guckenheimer, P Holmes 1983 Nonlinear Oscillations, DS, and Bifurcations of Vector Fields, Springer
JK Hale 1980 Ordinary DE 2ed, Wiley
MW Hirsch, S Smale 1974 DE, DS, and Linear Algebra, Academic Press
A Katok, B Hasselblatt 2005 A Moderna Teoria de Sistemas Dinâmicos, Fundação Calouste Gulbenkian
J Palis Jr, W de Melo 1978 Introdução aos Sistemas Dinâmicos, IMPA
L Perko 2006 DE and DS 3ed, Springer
M Shub 1987 Global Stability of DS, Springer
J Sotomayor 1979 Lições de Equações Diferenciais Ordinárias, IMPA
F Verhulst 1996 Nonlinear DE and DS 2ed, Springer
L Wen 2016 Differentiable DS, Am.Math.Soc.
Teaching Methodologies and Assessment Criteria The classes will be theoretical, practical and tutorial. The teacher presents the concepts, sets out the results, proving many of them. It further illustrates theory with examples and applications. The teacher points out texts from the bibliography for the student deepen their knowledge. The student is encouraged to participate in classes, interacting with the teacher and sometimes solving exercises and problems. Autonomous work is also encouraged, consisting mainly of exercises, problems and mathematical demonstrations. The evaluation carried out during the teaching-learning period will consist of two moments: Work (T) and presentation of a seminar (S). The final classification will be CF=(0.5*T+0.5*S). The student may also take a final exam.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2019-07-04

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