Lectures: TuesdayThursday, 11:00 am12:15 pm; PSY B50
Office Hours : TuTh 9:30am10:50am; 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 Homework 5, Due 12/7 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), 431438.
Blue sky catasstrophes in reversible and Hamiltonian systems
Ind. J. of Math. 26 (1977), 247263.
A. Barry, R. Hall, C.E. Wayne . Relative Equilibria of the (1+N)Vortex Problem
J. Non. Sci. 22 (2012), 6383.
K. Meyer, R. Hall, D. Offin Introduction to Hamiltonian Dynamical Systems and the NBody Problem
Springer. (2009).
P. Blanchard Complex analytic dynamics on the Riemann sphere
Bull. Amer. Math. Soc. 11 (1984), 85141.
T. Gallay C.E. Wayne . Invariant Manifolds and the LongTime Asymptotics of the NavierStokes and Vorticity Equations on R2
Arch. Rat. Mech. An.163 (2002), 209258.
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 NavierStokes equations
Notes.
M. Beck et. al. Snakes, Ladders, and Isolas of Localized Patterns
SIAM J. Math. Anal. 41 (2009), 936972.
M. Beck et. al. Using global invariant manifolds to undertand metastability in the Burgers equation with small viscosity.
SIAM Rev. 53 (2011), 129153.
A. Doelman, T. Kaper, P. Zegeling Pattern formation in the onedimensional GrayScott model
Nonlinearity 10 (1997).
C. Jones, T. Kaper, N. Kopell Tracking Invariant Manifolds up to Exponentially Small Errors.
SIAM J. Math. Anal. 27 (1996), 558577.
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), 403449.
N. Kopell, L. N. Howard Plane Wave Solutions to ReactionDiffusion Equations
Studies in Applied Math. 52 (1973), 291328.
Additional References
Papers mentioned in class:Grades
Your grades will based on homework (70%) and the project (30%).
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