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 1, Due 9/19 Homework 2, Due 10/3 Homework 3, Due 10/24 Homework 4, Due 11/14
ProjectSee 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
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
C.E. Wayne Lectures on dynamical systems and partial differential equations with applications to the Navier-Stokes equations
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 ReferencesPapers mentioned in class:
GradesYour grades will based on homework (70%) and the project (30%).
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