PUBLICATIONS:

1.Locating invariant sets, Proceedings of Symposia in Pure Mathematics, Vol. XIV,  American Math. Soc.,     55-59, (1969).

2.A flow near a degenerate critical point, Studies in Applied Mathematics, No. 5, SIAM, Philadelphia, PA, 1 p.(1969).

3.Isolated invariant sets and isolating blocks, (with C. Conley), Studies in Applied Mathematics, No. 5, SIAM, Philadelphia, PA, 97-104, (1969).

4On the existence of invariant sets inside a submanifold convex to a flow, Journal of Differential Equations, Vol. 7, No.1, 54-68, (1970).

5.Flows near isolated invariant set in dimension 3, Periodic orbits, stability and resonances, G.E.O. Giacoglia, Ed., D. Reidel Pub. Co., 332-336, (1970).

6.Isolated invariant sets and isolating blocks, (with C. Conley), Transactions of the American Mathematical Society, Vol. 158, No. 1, 35-61., (1971).

7.Regularization of vector fields by surgery, Journal of Differential Equations, Vol. 10, No. 1,  92-99, (1971).

8.Some topology of the 3-body problem, Journal of Differential Equations, Vol. 10,  No. 2, 371-377 (1971).

9.Isolating blocks, regularization and the 3-body problem, Proceedings of the International Symposium on Dynamical Systems, Salvador, Brazil, 75-96, (1971).

10.The topology of the regularized integral surfaces of the 3-body problem, Journal of Differential Equations, 361-384, (1972).

11.Isolating blocks and symbolic dynamics, Journal of Differential Equations, Vol. 17,  No. 1, 96-118, (1975).

12.Some topology of n-body problems, Journal of Differential Equations,

Vol. 19, No. 2, 258-269, (1975).

13.Some qualitative aspects of the 3-body flow, Dynamical Systems, An International Symposium, Vol. 2, Academic Press, Inc., 1-6, (1976).

14.Homoclinic phenomena in Hamiltonian systems with several degrees of freedom, Journal of Differential Equations, Vol. 29, No. 2, 241-252, (1978).

15.Chain transitivity and the domain of influences of an invariant set,

Lecture Notes in Mathematics, Vol. 668, Springer-Verlag, 95-102, (1978).

16.Homoclinic phenomena for orbits doubly asymptotic to an invariant three sphere, (with R. McGehee), Indiana J. of Mathematics, Vol. 28, No. 2, 211-140, (1979).

17.Perturbed twist maps, homoclinic points, and ergodic zones, Instabilities

in Dynamical Systems, V. Szebehely, Ed., D. Reidel Pub. Co., 41-49, (1979).

18.Ergodic properties of linked twist mappings, (with R. Burton), Lecture Notes in Mathematics, Vol. 819, Z. Nitecki and C. Robinson, Eds., Springer-Verlag, Inc., New York  35-49, (1980).

19.Homoclinic phenomena near orbits biasymptotic to invariant tori, Classical Mechanics and Dynamical Systems, R. Devaney, Z. Nitecki, Eds., Marcel Dekker, Inc., New York, 55-64, (1980).

20.Ergodic Theory and Hamiltonian Dynamics, Applications of Modern Dynamics

to Celestial Mechanics and Astrodynamics, V. Szebehely, Ed., D. Reidel Pub. Co., 267-277,  (1982).

21.Computing the dependence on a parameter of a family of unstable manifolds: Generalized Melnikov formulas, Journal of NonLinear Analysis:  Theory, Methods, and Applications, Vol. 8, No.1, 1-4, (1984).

22.Parabolic orbits in the planar 3-body problem, Journal of Differential Equations,

Vol. 52, No.1, 116-134, (1984).

23.Trellises formed by the stable and unstable manifolds of saddle points in the plane, Transactions of the American Mathematical Society, Vol 294, No. 2, 719-731, (1986).

24.Isolating Blocks and Epsilon Chains for Maps, Physica D, Vol. 39, No. 1, 95-110, (1989).

25.Transport through chaos, Nonlinearity 4. 583-590, (1991).

26.Capture orbits and Melnikov integrals in the planar 3-body problem,

Celestial Mechanics 50: 283-297, (1991).

27.Exit times and transport for symplectic twist maps, (with J. Meiss and S. Carver), Chaos Vol.3 No. 2, 153-165 (1993).

28.Transport of phase space volume near isolated invariant sets, Journal of Dynamics and Differential Equations, Vol. 5, No. 3, 529-536, (1993).

29.Geometric Methods for Discrete Dynamical Systems, Graduate Text, Oxford University Press (1998).

30.       Stability of Levitrons, (with H. Dullin), Physica D 126, 1-17 (1999) (Levitron2.pdf)

31.Stability of Levitrons, (with H. Dullin), Z. Angew. Math. Mech . Vol. 79, 167-170.

32.       Drift by Coupling to an Anti-Integrable Limit, (with J. D. Meiss and G. E. Roberts), Physica D. 156 201-218 (2001).

33.      Conley Index, in Encyclopedia of Nonlinear Science, Alwyn Scott Ed. Routledge, New York and London, 2005.

   

34.     Changing Climate, More Damaging Weather, Issues in Science and Technology, Vol. 26, No. 2 (2010), with Robert Repetto,

35.     Climate Change and Damages from Extreme Weather Events, Environment Vol. 52, No. 2 (2010), with Robert Repetto,.

36.     A Forest Village Model (January 2009) This is a model of a simple economy within an ecosystem. It is supplemented by an interactive Matlab program that allows the user to make a sequence of land use and labor allocation updates to see how the system responds.

37.     Financial Alchemy (2010). Manuscript for a book in progress.

38     Matlab programs (2010) for five increasingly complex economic models. These models supplement the Financial Alchemy manuscript.

39.     Finance Dynamics (2011). Manuscript of a short technical article.