KMA/DS1M Dynamical Systems 1

Lecturer: Irena Rachůnková, Jiří Fišer
Lecture: 2 hours/week e exercise 2 hours/week
Credits: 4
Summer semester
Form of course completion: course credit

• Autonomous differential equations and dynamical systems.
• Critical points, typical orbits. Phase portraits.
• Stability and asymptotical stability of critical points.
• Solutions of linear homogenenous systems with constant coefficients.
• Phase portraits of canonical systems.
• Classification of phase portraits of all linear systems with constant coefficients by eigenvalues.
• Topological classification.
• Nonlinear planar systems.
• Topological equivalence of systems near regular points.
• Topological equivalence of systems near hyperbolic critical points.
• Study of particular models.