Home Research Articles Proceedings and Books Research Announcements Research Articles On a system of equations in automatic control theory, Contributions to Differential Equations, III, 2, 1965, 163–173. A remark on a result of Lefschetz, Contributions to Differential Equations,III, 4, 1965, 435–37. Liapunov functions for the problem of Lur’e, Proceedings of the National Academy of Sciences, 53, 3, 1965, 501–03. On the existence of Liapunov functions for the problem of Lur’e, SIAM Journal on Control, 3, 3, 1966, 373–83. The condition of regular degeneration for singularly perturbed systems of linear differential–difference equations (with K.L. Cooke), Journal of Mathematical Analysis and Applications, 14, 1966, 83–106. Effect of delayed neutrons on the stability of a nuclear power reactor (with W. Baran), Nuclear Science and Engineering, 24, 1966, 356–61. On the existence of solutions to linear differential difference equations, Differential Equations and Dynamical Systems, Academic Press, New York, 1967, 239–45. Periodic points of diffeomorphisms, Bulletin American Mathematical Society,73, 5, 1967, 615–17. On contact transformations, American Journal of Physics, 35, 10, 1967, 970–71. A class of functional equations of neutral type (with J. K. Hale), Memoirs of the American Mathematical Society, 76, 1967. On computing the index in three dimensions , Proceedings of the American Mathematical Society, 19, 3, 1968, 760–63. Energy functions for Morse–Smale systems, American Journal of Mathematics, XC, 4, 1968, 1031–40. On the convergence of the zeta function for flows and diffeomorphisms, Journal of Differential Equations, 5, 2, 1969, 338–345. Subharmonic solutions in Hamiltonian systems, Seminar in Differential Equations and Dynamical Systems II, Lecture Notes in Mathematics 144, Springer–Verlag, 1969, 160–168. A new class of periodic solutions in the restricted three body problem (with J. Palmore), Journal of Differential Equations, 8, 2, 1970, 64–76. Generic bifurcation of periodic points, Transactions of the American Mathematical Society, 149, 1970, 95–107. A generic phenomenon in conservative Hamiltonian systems (with J. Palmore),Global Analysis, Proceedings of Symposia in Pure Mathematics, XIV, 1970, 185–89. Generic stability properties of periodic points, Transactions of the American Mathematical Society, 154, 1971, 273–77. Periodic orbits near L4 for mass ratios near the critical mass ratio of Routh (with D.S. Schmidt), Celestial Mechanics, 4, 1971, 99–109.Errata Stability of a Lur’e type equation, Symposium on Differential Equations, Lecture Notes in Mathematics 312, Springer Verlag, 1972, 145–50. Symmetries and integrals in mechanics, Dynamical Systems (Ed. M. Peixoto), Academic Press, New York, 1973, 259–72. Homoclinic points of area preserving diffeomorphisms (with R. McGehee), American Journal of Mathematics, 96, 3, 1974, 409–21. Canonical forms for symplectic and Hamiltonian matrices, (with Alan Laub), Celestial Mechanics, 9, 1974, 213–238. Generic Hamiltonian systems are neither integrable nor ergodic, (with L. Markus), Memoirs of the American Mathematical Society, 144, 1974. Normal forms for Hamiltonian systems, Celestial Mechanics, 9, 1974, 517–22. Implicit function theorem and analytic differential equations, Dynamical Systems – Warwick 1974, Lecture Notes in Mathematics 468, Springer–Verlag, 1975, 62–70. Adiabatic invariants for linear Hamiltonian systems (with A. Leung), Journal of Differential Equations, 17, 1, 1975, 32–43. Algebras of integrals (with U. Fong), Revista Colombiana de Mathematicas, IX, 1975, 75–90. Averaging and bifurcation in symmetric systems (with J. Henrard), SIAM Journal on Applied Mathematics, 32, 1, 1977, 133–45. Entrainment domains (with D.S. Schmidt), Funkcialaj Ekvacioj, 20, 2, 1977, 171–92. Periodic orbits and solenoids in generic Hamiltonian dynamical systems (with L. Markus), American Journal of Mathematics, 102, 1980, 25–92. Periodic orbits near infinity in the restricted N–body problem, Celestial Mechanics, 23, 1981, 69–81. The index sequence of a fixed point, Classical Mechanics and Dynamical Systems (Ed. Devaney and Nitecki), Marcel Dekker, New York, 1981, 159–71. Periodic solutions of the N–body problem, Journal of Differential Equations, 39, 1, 1981, 2–38. Hamiltonian systems with a discrete symmetry, Journal of Differential Equations, 41, 2, 1981, 228–38. An application of Poincare’s recurrence theorem to academic administration (a satire), American Mathematical Monthly, 88, 1, 1981, 32–33. Hill’s lunar equation and the three–body problem (with D.S. Schmidt), Journal of Differential Equations, 44, 2, 1982, 263–72. The determination of derivatives in Brown’s lunar theory (with D.S. Schmidt), Celestial Mechanics, 28, 1982, 201–07. Scaling Hamiltonian systems, SIAM Journal on Mathematical Analysis, 15, 5, 1984, 877–89. Normal forms for the general equilibrium, Funkcialaj Ekvacioj, 27, 2, 1984, 261–71. On the method of averaging, integral manifolds and systems with symmetries (with P.R. Sethna and A.K. Bajaj), SIAM Journal on Applied Mathematics, 45, 3, 1985, 343–59. Counter–examples in dynamical systems via normal form theory, SIAM Review, 28, 1, 1986, 41–51. The stability of the Lagrange triangular point and a theorem of Arnold (with D.S. Schmidt), Journal of Differential Equations, 62, 2, 1986, 222–36. Bifurcation of a central configuration, Celestial Mechanics, 40, 3, 1987, 271–82. An analytic proof of the shadowing lemma (with G. Sell), Funkcialaj Ekvacioj, 30, 1, 1987, 127–33. Bernoulli bundles and homoclinic phenomena in almost periodic systems ( with George Sell), Oscillations, Bifurcations and Chaos –CMS Conference Proceedings 8 (Ed. Atkinson, Langford and Mingarelli), AMS, Providence, Rhode Island, 1987, 527–44. Bifurcations of relative equilibria in the 4 and 5 body problems (with D. S. Schmidt), Ergodic Theory and Dynamical Systems,8*, 1988, 215–25. Bifurcations of relative equilibria in the N–body and Kirchhoff problems (with D. S. Schmidt), SIAM Journal on Mathematical Analysis, 19, 6, 1988, 1295–1313. An Anosov type stability theorem for almost periodic systems, Hamiltonian Dynamical Systems, Contemporary Mathematics 81, (K.R. Meyer and D. Saari, eds.), American Mathematical Society, Providence, R.I, 1988, 169–82. Melnikov transforms, Bernoulli bundles and skew product flows (with G. Sell), Transactions of the American Mathematical Society, 314, 1, 1989, 63–105. A new proof of and results related to Poincar´e’s center theorem, Differential Equations and Applications II (Ed. A. R. Aftabizadeh), Ohio University Press, Athens, Ohio, 1989, 202–209. A Lie transform tutorial–II, Computer Aided Proofs in Analysis (eds. K. R. Meyer and D. S. Schmidt), IMA Volumes in Mathematics and its Applications 28, Springer–Verlag, New York, 1991. The geometry of harmonic oscillators, The American Mathematical Monthly, 97(6), 1990, 457–465. Apollonus coordinates, the N–body problem, and continuation of periodic solutions, Journal of Dynamics and Differential Equations 3(3), 1991, 381–398. Global phase structure of the restricted isosceles three–body problem with pos–itive energy (with Qiudong Wang), Transactions of the American Mathematical Society 338(1), 1993, 311–336. Comet like periodic orbits in the N–body problem, Journal of Computational and Applied Mathematics, 52, 1994,337–51. Librations of central configurations and braided Saturn rings, (with D. S. Schmidt), Celestial Mechanics 55, 1993, 289–303. Perturbation analysis of nonlinear systems, Computer Algebra and Differential Equations (Ed. E. Tournier), London Mathematical Society Lecture Note Series 193, 1994, 103–140. The global phase structure of the three–dimensional isosceles three–body problem with zero energy, (with Qiudong Wang), Hamiltonian Dynamical Systems: History, Theory, and Applications, (Ed. H. S. Dumas, K. R. Meyer, and D. S. Schmidt), The IMA Volumes 63, Springer–Verlag, New York, 1995. The collinear three–body problem with negative energy, (with Qiudong Wang), Journal of Differential Equations,119(2),1995,284–309. Bifurcations of periodic solutions of Hamiltonian systems using fixed point methods, Differential Equations and Dynamical Systems, 3(1), 1995, 1–6. Limit periodic functions, solenoids, and adding machines (with H. Bell), Dynamics and Differential Equations 7(3), 1995, 409–422. Atomic spectroscopy, periodic orbits and generic two–parameter bifurcations, (with J. Delos and J. Mao), Conservative Systems and Quantum Chaos, (Ed. L. Bates and D. Rod), American Mathematical Society, Providence, R.I., 1996, 93–112. Equivariant generating functions for periodic points, New Trends in Hamiltonian Systems and Celestial Mechanics (Eds. E. Lacomba and J. Llibre), World Scientific, Sinapore, 1996, 289–300. Stability of skew dynamical systems (with J. Zhang), Journal of Differential Equations, 132(7), 1996, 66–86. Integral manifolds of the spatial three body problem, (with Christopher McCord and Qiudong Wang), Memoirs of the American Mathematical Society, 628, 1998, 1–91. Continuation of periodic solutions in three dimensions,, Physica D, 112(2), 1998, 310–318. The evolution of the stable and unstable manifold of an equilibrium point, Celestial Mechanics and Dynamical Astronomy, 70, 1998, 159–165. Bridges between the generalized Sitnikov family and the Lyapunov family of periodic orbits, (with Jaume Llibre and Jaume Soler), Journal of Differential Equations, 154, 1999, 140–156. Erratum. Stability of equilibria and fixed points of conservative systems (with H. Cabral), Nonlinearity, 12, 1999, 1351–1362. From the restricted to the full three–body problem (with D. Schmidt), Transactions of the American Mathematical Society, 352(5), 2000, 2283–2299. Doubly–symmetric periodic solutions of the spatial restricted three–body problem, (with R. Clarissa Howison), Journal of Differential Equations, 163, 2000, 174–197. Cross sections in the spatial three–body problem (with C. McCord), Journal of Dynamics and Differential Equations, 12(2), 2000, 247–271. Doubly symmetric periodic solutions of Hill’s lunar problem, (with R. Clarissa Howison), Hamiltonian Systems and Celestial Mechanics (HAMSYS–98), (Eds. J Delgado, E. A. Lacomba, E. P´erez–Chavela, and J. Llibre), World Scientific Monograph Series, Volume 6, Singapore, 2000, 186–196. Integral manifolds of the restricted three–body problem (with C. McCord), Ergodic Theory and Dynamical Systems, 21, 2001, 885–914. Jacobi elliptic functions from a dynamical systems point of view, American Mathematical Monthly, 108(8), 2001, 729-737. Are Hamiltonian flows geodesic flows?, (with C. McCord and D. Offin), Transactions of the American Mathematical Society, 355(3), 2002, 1237–1250. The evolution of invariant manifolds in Hamiltonian Hopf bifurcations, (with P. McSwiggen), Journal of Differential Equations, 189, 2003, 538–555. Stability and bifurcation for the N+ 1 vortex problem on the sphere, (with H. Cabral & D. Schmidt), Regular and Chaotic Dynamics, 8(3), 2003, 259–282. Elliptic relative equilibria in the N–Body problem, (with D. Schmidt), Journal of Differential Equations, 214, 2005, 256-298. Phase portraits of linear differential equations, (with P. McSwiggen), American Mathematical Monthly, 115(7), 2008, 596-614. Periodic solutions in Hamiltonian systems, averaging, and the lunar problem, (with P. Yanguas, J. Palacian and S. Dumas), SIAM Journal on Applied Dynamical Systems, 7(2), 2008, 311-340. Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities, (with X. Hou, Y. Li), Discrete and Continuous Dynamical Systems A, 26(1),2010, 265-290. Bifurcation of heteroclinic orbits, (with P. McSwiggen and X. Hou), The Journal of Dynamics and Differential Equations, 22(3), 2010, 367-380. Geometric averaging of Hamiltonian systems: periodic solutions, stability, and KAM tori, (with J. Palacian and P. Yanguas), SIAM Journal on Applied Dynamical Systems, 10(3), 2011, 817-856. Normally Stable Hamiltonian systems, (with J. Palacian and P. Yanguas), Discrete and Continuous Dynamical Systems, 33(3), 2013, 1201-1214. Stability of a Hamiltonian system in a limiting case, (with J. Palacian and P. Yanguas), Regular and Chaotic Dynamics, 17(1),2012,24-35. Invariant tori in the lunar problem, (with J. Palacian and P. Yanguas), Publicacions Matemàtiques, Proceedings of the Conference New Trends in Dynamical Systems, 2014, 353-394. The elusive Liapunov periodic solutions, (with J. Palacian and P. Yanguas), Qualitative Theory of Dynamical Systems, 14, 2015, 381-401. Asymptotic stability estimates near an equilibrium point, (with H. S. Dumas, J. Palacian and P. Yanguas), Journal of Differential Equations, 263, 2017, 1125-1139. Bounding solutions of a forced oscillator, (with D. S. Schmidt), Journal of Dynamics and Differential Equations. Singular reduction of resonant Hamiltonians, (with J. Palacian and P. Yanguas), Nonlinearity, 31, 2018, 2854-2894. Normalization Through Invariants in n-Dimensional Kepler Problems, (with J. Palacian and P. Yanguas), Regular and Chaotic Dynamics, 23(4), 2018, 389-417. The evolution of invariant manifolds II, (with D. S. Schmidt), manuscript. Proceedings and Books Hamiltonian Dynamical Systems , Contemporary Mathematics 81, (with D. Saari), American Mathematical Society, Providence, R.I, 1988. Computer Aided Proofs in Analysis, (with D. S. Schmidt), IMA Volumes in Mathematics and its Applications 28, Springer–Verlag, New York, 1991. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, (with G. R. Hall), Springer–Verlag, New York, 1992. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 2nd Edition, (with G. R. Hall and D. Offin), Springer, 2009. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, 3ed Edition, (with D. Offin), Springer, 2009. Twist Mappings and Their Applications, (with R. McGehee), IMA Volumes in Mathematics and its Applications 44, Springer–Verlag, New York, 1992. Hamiltonian Dynamical Systems: History, Theory, and Applications,(Ed. H.S. Dumas, K. R. Meyer, and D. S. Schmidt), The IMA Volumes 63, Springer–Verlag, New York, 1995. Periodic Solutions of the N–Body Problem, Lecture Notes in Mathematics 1719, Springer–Verlag, 1999. Research Announcements Generic Hamiltonian systems are not ergodic (with L. Markus), Proceedings of the 5th International Conference on Nonlinear Oscillations, Kiev, 1969, 304–10. Canonical forms for critical points, Seminar on Differential Equations and Dynamical Systems III, University of Maryland Seminar Series No. 15, 1970-71, 55-64. Homoclinic points of area preserving maps and Generic bifurcation in Hamiltonian systems, Warwick Dynamical Systems –1974, Lecture Notes in Mathematics, Springer–Verlag, 62–70. Adiabatic invariants for linear Hamiltonian systems (with A. Leung), Geometrie Symplectique et Physique Mathematique, (Ed. J. M. Souriau), Centre National de la Recherche Scientifique, Paris, 1975, 137–45. Solenoids in generic Hamiltonian dynamics ( with L. Markus), Research in Ordinary Differential Equations and Fixed Point Properties, Kyoto University, Kyoto, Japan, 1976, 1–16. Entrainment domains (with D. S. Schmidt), Proceedings of the 8th International Conference on Nonlinear Oscillations, Prague, 1978, 479–81. Tori in resonance, IMA Preprint Series 13, University of Minnesota, 1983. Bibliographic notes on generic bifurcations in Hamiltonian systems, Multiparameter Bifurcation Theory, Contemporary Mathematics 56, (M. Golubitsky and J. Guckenheimer, eds.), American Mathematical Society, Providence, R.I, 1986, 373-381. Bifurcations of central configurations in the N–body problem, (with D. S. Schmidt), Mathematics of Nonlinear Science (Ed. M. Berger ), American Mathematical Society, Providence, R.I., 1990, 93–101. Notes on Delaunay and Poincar\'e Elements, (with C. Howison), University of Cincinnati Lecture Notes, 1995.