Benettin, G., Galgani, L., and Streleyn, J.-M. (1976).
Phys. Rev. A 14, 2338.
Brouwer, D., and Van Woerkom, A.J.J. (1950). Astron.
Papers Amer. Eph. Naut. Almanac 13, 81.
Chirikov, B.V. (1979). Phys. Rep. 52, 263.
Chirikov, B.V., and Shepelyansky, D.L. (1984a). Proc.
9th Int. Conf. on Nonlinear Oscillations (Kiev),
Vol. II (Naukova Dumka, Kiev). English transla-
tion: Plasma Physics Lab. Rep. PPPL-TRANS-133,
Princeton Univ.
Chirikov, B.V., and Shepelyansky, D.L. (1984b).
Physica D 13, 395.
Danby, J.M.A. (1988). Fundamentals of Celestial
Mechanics, 2nd edition, Willmann-Bell,
Richmond.
Franklin, F., Lecar, M., and Murison, M. (1993).
Astron. J., 105, 2336.
Giorgilli, A. (1988). Ann. Inst. Henri Poincare 48 A,
423.
Giorgilli, A., Delshams, E., Foutich, E., Galgani, L.,
and Simo, C. (1989). J. Diff. Eq. 77, 167.
Holman, M.J., and Wisdom, J. (1993). Astron. J. 105,
1987.
Jensen, R.V. (1984). Phys. Rev. A 30, 386.
Kaneko, K., and Konishi, T. (1994). Physica D 71,
146.
Karney, C.F.F., (1983). Physica D 8, 360.
Lai, Y.C., Grebogi, C., Blumel, R., and Ding, M.
(1992). Phys. Rev. A 45, 8284.
Laskar, J. (1989). Nature 338, 237.
Lecar, M., and Franklin, F. (1973). Icarus 20, 422.
Lecar, M., Franklin, F., and Soper, P. (1992a). Icarus
96, 234.
Lecar, M., Franklin, F., and Murison, M. [LFM]
(1992b). Astron. J. 104, 1230.
Levison, H.F., and Duncan, M.J. (1992). Preprint.
Lichtenberg, A.J., and Lieberman, M.A. (1992).
Regular and Chaotic Dynamics, 2nd ed., Springer-
Verlag, New York.
MacKay, R.S., Meiss, J.D., and Percival, I.C. (1984).
Physica D 13, 55.
Mikkola, S., and Innanen, K. (1992). Astron. J. 104,
1641.
Milani, A., and Nobili, A. (1992). Nature 357, 569.
Murison, M., (1989). Astron. J. 97, 1496.
Murray, N.W. (1991). Physica D 52, 220.
Nekhoroshev, N.N. (1977). Russ. Math. Surv. 32, 5.
Percival, I.C. (1979). In Nonlinear Dynamics and the
Beam-Beam Interaction, eds. M. Month and J.C.
Herrera, Am. Inst. of Physics Conf. Proc. No. 57.
Perry, A.D., and Wiggins, S. (1994). Physica D 71,
102.
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vet-
terling, W.T. (1992). Numerical Recipes in C: The
Art of Scientific Computing, 2nd edition, Cam-
bridge Univ. Press, New York.
Soper, P., Franklin, F., and Lecar, M. (1990). Icarus
87, 265.
Stoer, J., and Bulirsch, R. (1980). Introduction to
Numerical Analysis, Springer-Verlag, New York.
Sussman, G.J., and Wisdom, J. (1988). Science 241,
433.
Sussman, G.J., and Wisdom, J. (1992). Science 257,
56.
Szebehely, V. (1967). Theory of Orbits, Academic,
New York.
Szebehely, V., and Giacaglia, G.O. (1964). Astron. J.
69, 230.
Torbett, M.V. (1989). Astron. J. 98, 1477.
Wiggins, S. (1990). Introduction to Applied Nonlinear
Dynamical Systems and Chaos, Springer-Verlag,
New York.
Wisdom, J. (1983). Icarus 56, 51.
Wolf, A., Swift, J.B., Swinney, H.L., and Vasano, J.A.
(1985). Physica D 16, 285.
REFERENCES
J
case clearly show that
some bodies further than ~2
from the relation
are present. We suggest, therefore, that the
minor planets in the outer belt with short T
L
(and T
e
< T
SS
) are the counterparts of these
bodies for the real, 1 M
J
case.
We thank Brian Marsden and Gareth
Williams of the Minor Planet Center for their
usual cheerful and prompt responses to
requests for asteroid ephemerides.
Chaotic Motion in the Outer Asteroid Belt
page 13