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12819 Dynamic systems. Qualitative Theory - Five-year degree in Mathematics

Center

Faculty of Mathematics

Departament

Applied Mathematics

Lecturers in charge

Sin datos cargados

Met. Docent

Met. Avaluació

Final examination and project work

Bibliografia

Referències bàsiques:

Arnold V.I., Equations Différentielles Ordinaires, Mir, Moscou, 1974.
Braun M., Differential Equations and Their Applications, 4th Edition, Springer-Verlag, 1993.
Clark A., DynPac. A Dynamical System Package for Mathematica 4. Department of Mechanical Engineering. University of Rochester. Revision 10.60. Juliol, 2000.
Hale J., Koçak H., Dynamics and Bifurcations, volum 3 de Texts in Applied Mathematics. Springer-Verlag, New York, 1991.
Hartman, P., Ordinary Differential Equations, Wiley, New-York, 1964
Hüseyin Koçak. Differential and Difference Equations through Computer Experiments. Springer-Verlag, New York, 1989.
Kathleen T. Alligood, Tim D. Sauer, James A. Yorke. Chaos. An introduction to Dynamicals Sy

Continguts

Objectives
The objective of the subject is to describe the qualitative (or geometric) behaviour of a set of solutions of a system of differential equations given, that is to say, knowledge of the most relevant properties of a system (stability, asintotic behaviour, etc.) without knowing the solutions explicitly. To achieve this we will study the analytical, geometric topological and numerical operations that are used in analysing the local and global properties of the solutions of differential equations.