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Course description. APMA 2190 is a graduate-level introduction to nonlinear dynamical systems. Topics covered include basic existence and uniqueness results for ordinary differential equations, linear systems and Floquet theory, hyperbolicity, topological conjugacies, the Grobman-Hartman theorem, stable and unstable manifold theorems, planar systems and the Poincaré-Bendixson theorem, center manifolds, bifurcation theory, and Hamiltonian systems.
Occasionally we may also discuss various generalizations to infinite-dimensional dynamics and applications to partial differential equations.
Useful references. Although there is no required text, the following, among others, may be useful in parts of the course:
- Luis Barreira and Claudia Valls, Ordinary differential equations: Qualitative theory, AMS
- Carmen Chicone, Ordinary differential equations with applications, Springer
- Philip Hartman, Ordinary differential equations, 2nd Edition, SIAM
- Herbert Amann, Ordinary differential equations, de Gruyter
Grading policy: The final grade will be based on homework assignments and a take-home final exam:
Homework assignments: Homework problems will be handed out on a regular basis. Discussion of homework assignments with other students is encouraged, but what is handed in should be your own work.
Accommodations: Brown University is committed to full inclusion of all students. Please inform me early in the term if you have a disability or other conditions that might require accommodations or modification of any of these course procedures. You may speak with me after class or during office hours. For more information, please contact Student and Employee Accessibility Services at 401-863-9588 or SEAS@brown.edu.
Students in need of short-term academic advice or support can contact one of the deans in the Dean of the College office.
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
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