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From: riddle@mathcs.emory.edu (Larry Riddle)
Newsgroups: sci.math,comp.theory.dynamic-sys
Subject: chaos in astronomy (summary)
Keywords: chaos, dynamical systems, astronomy
Message-ID: <6628@emory.mathcs.emory.edu>
Date: 7 Dec 90 02:09:33 GMT
Followup-To: poster
Organization: Math & Computer Science, Emory University, Atlanta, GA
Lines: 55


Two weeks ago I posted a request for references about the use of chaos
and dynamical systems in astronomy. I would like to thank everyone who
responded. Following is a summary of those responses. I have not had a
chance to investigate every reference so some are still a bit vague.

1. Chaotic Phenomena in Astrophysics, J.R. Buckler & H.Eichhorn, eds.,
Annals of the New York Academy of Sciences, vol 497, 1987

2. Paper by G. Sussman and J. Wisdom on the chaotic nature of Pluto's
orbit in Scientific American about two years ago.

3. The work of Jack Widsom on the digital orrery and the applications of
Bowen's shadowing theorem for the control of spacecrafts. Reference is
Science, vol 241, p 433 (1988). Control of spacecrafts is topic of James
Yorke who will have an article in the proceedings of the CNLS annual
conference to be published as a special issue of Physics D.

4. The three body problem (mentioned by several people) 
* books ofAbraham and Marsden, Gutzwiller, and vol one of Thirrings' course in
mathematical physics.
* Poincare's 3-volume "New Methods in CelestrialMechanics" (1890s) 
* Rick Moeckel, "Hamiltonian Dynamical Systems",Contemporary Math., v. 81.
* Birkoff's book "Dynamical Systems", AMS, circe 1920's (republished in the
60's 

5. Berry, Topics in Nonlinear Dynamics, ed S. Jorna, Am. Inst. Conf.
Proc. 46 (1978) (available through the APS) - why are the rings of
Saturn where they are?

6. "Simple Dynamical Models of Neptune's Great Dark Spot", L.M. Polvani,
J. Wisdom, E. DeJong, A.P. Ingersoll, Science, 21st Sept, 1990, vol 249,
1393-1398

7. "Chaotic Motion of Europa and Ganymede and the Ganymede-Callisto
Dichotomy", William C. Tittlemore, Science, 12 Oct. 1990, vol 250,
263-267

8. Article on the origin of the gaps in Saturn's rings and a nice
article by Moser in the Intelligencer in about 1984

9. Survey of Henon-Heiles by Churchill and Rod in SLN Phys 93

10. Chaos: How regular can it be? Physics Today, November 1988, p27


Larry Riddle        | riddle@mathcs.emory.edu         PREFERRED
Agnes Scott College | {decvax,gatech}!emory!riddle    UUCP 
Dept of Math        | riddle@emory.bitnet             NON-DOMAIN BITNET
Decatur, GA 30030   | (404) 371-6222                  AT&T
-- 
Larry Riddle        | riddle@mathcs.emory.edu         PREFERRED
Agnes Scott College | {decvax,gatech}!emory!riddle    UUCP 
Dept of Math        | riddle@emory.bitnet             NON-DOMAIN BITNET
Decatur, GA 30030   | (404) 371-6222                  AT&T


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