Applied Mathematics 8100

Seminar on Dynamical Systems

Thursdays, 3PM, ECOT 226

For Spring Semester 1997 we had a number of informal seminars by locals and visitors including

Lora Billings
Mark Werner
Robert Easton
David Sterling
Bruce Peckham
Sir Michael Berry
Hector Lomeli
Joe Iwanski
Holger Dullin

In the Fall '96, the seminar was run as a journal club. Attendees are required to do the reading for each meeting, and actively participate in the discussion. The papers we read will be chosen, pseudo-democratically (i.e. some of us have veto power!), by the active members of the seminar.

Fall 96 Reading List

Sept 12 Chaos in Ecology: Is Mother Nature a Strange Attractor?, A. Hastings, C. Hom, S. Ellner, P. Turchin, H. Godfray, Ann. Rev. Ecol. Sys 24,1-33(1993).
Sept19 The Spatial Dilemmas of Evolution M. Nowak and R. May, Int. J. of Bif. and Chaos 3,35-78(1993).
Oct3&10 Intermingled Basins for the Triangle Map, J. Alexander, B. Hunt, I. Kan, and J. Yorke, Erg. Th. Dyn. Sys. 16,631-662 (1996).
Oct 17 Frequency Analysis J. Laskar, Physica D
Rotation Vectors for Maps on the n-Torus Miscerewicz.

Should you be interested, these papers are in a box in the conference room.

References we've read or considered in the past include

Off to Infinity in Finite Time, D. Saari and Z. Xia*
Mathematical Complexity of Simple Economics, D. Saari, preprint (1991).&
Symplectic Calculation of Lyapunov Exponents, S. Habib, R. Ryne, Phys. Rev. Lett, 74, 70-73 (1995).*
Coupled Oscillators and the Design of Central Pattern Generators, N. Kopell, G.B. Ermentrout, Math. Biosciences 90, 87-109 , 1988,*
Symmetry and Phaselocking in Chains of Weakly Coupled Oscillators N. Kopell, G.B. Ermentrout, Comm. Pure Appl. Math 29 623-660, 1986*
Progress in the Control of Chaos, T. Shinbrot, Adv. in Phys. 44, 73-111 (1995).
Integrable Symplectic Maps, M Bruschi, O. Ragnisco, P.M. Santini and T. Ghi-Zhanng, Physica D 49, 273-294 (1991).
Stability Theory for Dissipatively Perturbed Hamiltonian Systems, J. Maddocks and M.L. Overton, preprint (1994).
Regularization in Celestial Mechanics, V. Szebehely.
Dynamical Systems, V.S. Afraimovich, L.A. Bunimovich, J.K.Hale, preprint, 1995.
Hyperbolic Tori and Asymptotic Surfaces in Hamiltonian Systems, D. Treshev, Rus. J. of Math. Phys. 2, 93-110 (1994).
Lindstedt Series, Ultraviolet Divergences and Moser's Theorem F. Bonetto, G. Gallavotti, G. Gentile, V. Mastropietro, IHES Preprint, 1995.
Plotting Stable Manifolds: Error Estimates and Noninvertible Maps, E. Kostelich, J. A. Yorke, Z. You, Phyisca D, in press, 1995.
Effective Stability and KAM Theory, A. Delshams and Pere Gutierrez, Univ. Potitecnica de Catalunya, 1995.*
Embedology T. Sauer, J. Yorke, M. Casdagli, J. Stat. Phys. 65, 95-116 (1991).*
A topological Version of a Theorem of Mather on Twist Maps, G.R. Hall, Ergod. Th. & Dyn. Sys. 4, 585-603 (1984).*

Participants: Send your suggestions to Jim Meiss.

* Papers read in earlier semesters