This is the second semester of a graduate level introduction to differential equations and dynamical systems with emphasis on qualitative, geometrical methods for nonlinear systems.
Topics for the second semester include: linearization, Hartman's theorem, normal forms, Hopf bifurcation, limit sets, gradient-like systems, Lagrangian and Hamiltonian systems, existence, continuation and stability of periodic orbits, Poincaré maps and discrete dynamical systems; homoclinic points and homoclinic chaos, circle maps and rotation numbers; introduction to ergodic theory.
| "Dynamical Systems: Stability, Symbolic Dynamics and Chaos", by Clark Robinson |
| "Ordinary Differential Equations with Applications", by C. Chicone |
| "Ordinary Differential Equations", by V.I. Arnold |
| "Lectures on Ordinary Differential Equations", by W. Hurewicz |
| "Ordinary Differential Equations", by Jack Hale |
| "Differential Equations, Geometric Theory", by S. Lefschetz |
| "Ordinary Differential Equations", by Philip Hartman |
| "Theory of Ordinary Differential Equations", by E. Coddington and N. Levinson |
Based on several homework assignments throughout the semester. No exams. The link leads to PDF versions of the homework assignments.
| Homework | 100 % |