MA 775 Ordinary Differential Equations

MA 775 - Ordinary Differential Equations

Course Information

Lectures: Tuesday-Thursday, 11:00 am-12:15 pm; PSY B50
Office Hours : TuTh 9:30am-10:50am; or by appointment.
Syllabus: PDF here

Homework

  • Homework 1, Due 9/19
  • Homework 2, Due 10/3
  • Homework 3, Due 10/24
  • Homework 4, Due 11/14
  • Project

    See the syllabus for more detail. Below are links to some suggested papers:
    R. Devaney . Homoclinic orbits in Hamiltonian systems
    J. Diff. Eq. 21 (1976), 431-438.
    Blue sky catasstrophes in reversible and Hamiltonian systems
    Ind. J. of Math. 26 (1977), 247-263.
    A. Barry, R. Hall, C.E. Wayne . Relative Equilibria of the (1+N)-Vortex Problem
    J. Non. Sci. 22 (2012), 63-83.
    K. Meyer, R. Hall, D. Offin Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
    Springer. (2009).
    P. Blanchard Complex analytic dynamics on the Riemann sphere
    Bull. Amer. Math. Soc. 11 (1984), 85-141.
    T. Gallay C.E. Wayne . Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2
    Arch. Rat. Mech. An.163 (2002), 209-258.
    J.P. Eckmann C.E. Wayne Propagating fronts and the center manifold theorem
    Comm. Math. Phys. 136 (1991).
    C.E. Wayne An Introduction to KAM Theory
    Notes.
    C.E. Wayne Lectures on dynamical systems and partial differential equations with applications to the Navier-Stokes equations
    Notes.
    M. Beck et. al. Snakes, Ladders, and Isolas of Localized Patterns
    SIAM J. Math. Anal. 41 (2009), 936-972.
    M. Beck et. al. Using global invariant manifolds to undertand metastability in the Burgers equation with small viscosity.
    SIAM Rev. 53 (2011), 129-153.
    A. Doelman, T. Kaper, P. Zegeling Pattern formation in the one-dimensional Gray-Scott model
    Nonlinearity 10 (1997).
    C. Jones, T. Kaper, N. Kopell Tracking Invariant Manifolds up to Exponentially Small Errors.
    SIAM J. Math. Anal. 27 (1996), 558-577.
    N Kopell,et. al. Gamma rhythms and beta rhythms have different synchronization properties
    Proc. Nat. Acad. Sci. 97 (2000).
    D.G. Aronson, G.B. Ermentrout, N. Kopell Amplitude response of coupled oscillators.
    Physica D 41 (1990), 403-449.
    N. Kopell, L. N. Howard Plane Wave Solutions to Reaction-Diffusion Equations
    Studies in Applied Math. 52 (1973), 291-328.

    Additional References

    Papers mentioned in class:

    Grades

    Your grades will based on homework (70%) and the project (30%).
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