Publications
Journal Articles
, A stable manifold theorem for degenerate fixed points with applications to celestial mechanics, J. Differential Equations 14 (1973), 70-88. doi:10.1016/0022-0396(73)90077-6
, Homoclinic points of area-preserving diffeomorphisms, Amer. J. Math. 96 (1974), 409-421. doi:10.2307/2373550
, Triple collision in the collinear three-body problem, Inventiones Math. 27 (1974), 191-227. doi:10.1007/BF01390175
, Coexistence of two competitors on one resource, J. Theor. Biol. 56 (1976), 499-502. doi:10.1016/S0022-5193(76)80089-6
, Coexistence of species competing for shared resources, Theor. Pop. Biol. 9 (1976), 317-328. doi:10.1016/0040-5809(76)90051-4
, Some mathematical problems concerning the ecological principle of competitive exclusion, J. Differential Equations 23 (1977), 30-52. doi:10.1016/0022-0396(77)90135-8
, Homoclinic Phenomena for Orbits Doubly Asymptotic to an Invariant Three Sphere, Indiana U. Math. J. 28 (1979), 211-240. doi:10.1512/iumj.1979.28.28015
, Competitive Exclusion, The American Naturalist 15 (1980), 151-170. doi:10.1086/283553
, Double collisions for a classical particle system with nongravitational interaction, Comment. Math. Helvetici 56 (1981), 524-557. doi:10.5169/seals-43257
, Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study, Comm. Math. Phys. 83 (1982) 304-354. doi:10.1007/BF01213607
, Entrainment regions for periodically forced oscillators, Phys. Rev. A 33 (1986) 2190-2192. doi:10.1103/PhysRevA.33
, Von Zeipel's theorem on singularities in celestial mechanics, Expositiones Mathematicae 4 (1986), 335-345.
, Charles C. Conley 1933-1984, Ergodic Theory and Dynamical Systems 8* (1988), 1-7. doi:10.1017/S0143385700009287
, Attractors for closed relations on compact Hausdorff spaces, Indiana U. Math. J. 41 (1992) , 1165-1209. doi:10.1512/iumj.1992.41.41058
, Resonance surfaces for forced oscillators, Experimental Math. 3 (1994), 223-244. doi:10.1080/10586458.1994.10504292
, A new proof of the stable manifold theorem, Z. angew. Math. Phys. 47 (1996), 497-513. doi:https://doi.org/10.1007/BF00914867
, Arnold flames and resonance surface folds, International Journal of Bifurcation and Chaos 6 (1996), 315-336. doi:10.1142/S0218127496000072
Conley Decomposition for Closed Relations, Journal of Difference Equations and Applications 12 (2006), 1-47. doi:10.1080/00207210500171620
A Paleoclimate Model of Ice-Albedo Feedback Forced by Variations in Earth’s Orbit, SIAM J. Applied Dynamical Systems 11 (2012), 684-707. doi:10.1137/10079879X
, Modeling Climate Dynamically, The College Mathematics Journal 44 (5) (2013), 350-364. doi:10.4169/college.math.j.44.5.350
, A Quadratic Approximation to Budyko’s Ice-Albedo Feedback Model with Ice Line Dynamics, SIAM Journal on Applied Dynamical Systems 13 (1) (2014), 518-536. doi:10.1137/120871286
, Classification of critical sets and their images for quadratic maps of the plane, Journal of Difference Equations and Applications 22 (5) (2016), 637-655. doi:10.1080/10236198.2015.1127360
, Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles, Nonlinearity 29 (6) (2016), 1843-1864. doi:10.1088/0951-7715/29/6/1843
, Nonsmooth frameworks for an extended Budyko model, Discrete & Continuous Dynamical Systems Series B 22 (2017), 2447-2463. doi:10.3934/dcdsb.2017125
, A simple formula for a planet’s mean annual insolation by latitude, Icarus 291 (2017), 46-50. doi:10.1016/j.icarus.2017.01.040
, Approximating Annual Mean Incoming Solar Radiation, J. Math. Anal. Appl. 500 (1) (2021). doi:10.1016/j.jmaa.2021.125129
, Intensity—A Metric Approach to Quantifying Attractor Robustness in ODEs, SIAM Journal on Applied Dynamical Systems 21 (2) (2022). doi: 10.1137/20M138689X
Articles in Conference Proceedings
, Parabolic orbits in the three-body problem, Dynamical Systems (M. M. Peixoto, ed.), Academic Press, New York (1973), 249-254.
, The stable manifold theorem via an isolating block, Symposium on Ordinary Differential Equations (W. Harris & Y. Sibuya, eds.), Lecture Notes in Mathematics 312, Springer-Verlag, Berlin (1973), 135-144.
, Dynamical Systems, Theory and Applications (J. Moser, ed.), Lecture Notes in Physics 38, Springer-Verlag, Berlin (1975), 550-572.
, Solutions of the collinear four-body problem which become unbounded in finite time, Dynamical Systems, Theory and Applications (J. Moser, ed.), Lecture Notes in Physics 38, Springer-Verlag, Berlin (1975), 573-597.
, Singularities in classical celestial mechanics, Proceedings of the International Congress of Mathematicians Helsinki 1978, 827-834.
, A discrete dynamical system with subtly wild behavior, New Approaches to Nonlinear Problems in Dynamics, (P. Holmes, ed.), SIAM (1980), 339-359.
, Resonance phenomena for two parameter families of maps of the plane: uniqueness and nonuniqueness of rotation numbers, Nonlinear Dynamics and Turbulence (Barenblatt, Iooss, & Joseph, ed.), Pitman, Boston (1983), 35-47.
, A Note on the Moser-Hald Variation of Newton's Method, Analysis, et cetera: Research Papers Published in Honor of Jurgen Moser's 60th Birthday (P. Rabinowitz & E. Zehnder, eds.), Academic Press, Boston (1990), 495-499.
, Determining the Global Topology of Resonance Surfaces for Periodically Forced Oscillator Families, Proceedings of the Workshop on Normal Forms and Homoclinic Chaos, Fields Institute Communications 4 (1995), AMS, 233-251.
Books Edited
Charles Conley Memorial Volume, Cambridge University Press, Cambridge, 1988.
Twist Mappings and their Applications, The IMA Volumes in Mathematics and its Applications 44, Springer-Verlag, Berlin, 1992.
Unpublished Reports
, A nonsingular list structure for multiprocessor systems, CPT Research Report No. 0482 (1984).
A proof of the Mandelbrot N-squared conjecture, Institut Mittag-Leffler Report No. 15 (1984).
Some Metric Properties of Attractors with Applications to Computer Simulations of Dynamical Systems, October 1988.
Carbon Negativity Estimates for Grassland Biomass, February 16, 2007.
, A simplification of Budyko's ice-albedo feedback model, March 2012.