||8 credit points
||Diekmann, O. (Universiteit Utrecht), Kuznetsov, Yu.A. (Universiteit Utrecht)
||The aim of this course is to introduce basic ideas, concepts, examples, results, techniques and methods for studying the orbit structure of smooth dynamical systems on finite dimensional spaces generated by ordinary differential equations (ODEs) or iterated maps.
||Subjects that will be treated in detail are:
-- linearization near steady states: the Principle of Linearized Stability and local topological equivalence (the Grobman-Hartman Theorem)
-- phase plane analysis: Poincare-Bendixson theory, planar Hamiltonian systems from mechanics and their perturbations, predator-prey systems
-- bifurcation theory (how does the orbit structure change when a parameter is varied) for ODE and for maps
-- stability of periodic solutions of ODE (Poincare' maps and Floquet multipliers)
-- combined Center Manifold and Normal Form reduction
-- the horseshoe map and symbolic dynamics (and chaotic behaviour)
||2 x 45 min lectures + 45 min exercise session per week.
The course material includes pencil-and-paper exercises and exercises that require the use of symbolic manipulation tools, such as MAPLE, as well as simple simulation programs. There are no weekly home assignments.
||At the end of the course a take-home examination problem will be posted. The students should take 7 to 8 days in a period of 3 weeks to produce a written elaboration, which contributes 40% to the final grade. The remaining 60% of the grade are coming from a written examination.
||- Yu.A. Kuznetsov. Elements of Applied Bifurcation Theory. 3rd ed. Springer-Verlag, New York, 2004 (optional)
- F. Verhulst. Nonlinear Differential Equations and Dynamical Systems. Springer, Universitext, 1996 (optional)
- Lecture notes and computer session manuals available on-line during the course.
Any standard Bachelor course on OD's with proofs.
||Please visit: http://www.staff.science.uu.nl/~kouzn101/NLDV/index.html