Chapters in Books
Hopf bifurcation and the method of averaging, (with S.-N. Chow), Chap. 4C of The Hopf Bifurcation, by J. Marsden and M. McCracken, Applied Math. Sciences, Vol. 19, Springer–Verlag, New York, 1976.
Refereed Publications
Generic properties of retarded functional differential equations, Bull. Amer. Math. Soc. 81 (1975), 750–752.
Generic periodic solutions of functional differential equations, Jour. Diff. Eq. 25 (1977), 163–183.
Negatively invariant sets of compact maps and an extension of a theorem of Cartwright, Jour. Diff. Eq. 22 (1976) 331–348.
Applications of generic bifurcation, I, (with S.-N. Chow and J.K. Hale), Arch. Rat. Mech. Anal. 59 (1975), 159–188.
Applications of generic bifurcation, II, (with S.-N. Chow and J.K. Hale), Arch. Rat. Mech.Anal. 62 (1976), 209–235.
Integral averaging and bifurcation, (with S.-N. Chow), Jour. Diff. Eq. 26 (1977), 112–159.
The Fuller index and global bifurcation, (with S.-N. Chow), Jour. Diff. Eq. 28 (1978), 66–85.
Buckling of cylindrical shells with small curvature, Quart. Appl. Math. 35 (1977), 383–400.
Finding zeros of maps: Homology methods that are constructive with probability one, (with S.-N. Chow and J.A. Yorke), Math. Comp. 32 (1978), 887–899.
Global Hopf Bifurcation from a Multiple Eigenvalue (with S.-N. Chow and J.A. Yorke), J. Nonlinear Anal. 2 (1978), 753–763.
A homotopy method for locating all zeros of a system of polynomials (with S.-N. Chow and J.A. Yorke) Functional differential equations and approximation of fixed points, Springer–Verlag Lecture Notes in Mathematics, Vol. 730 (1979), pp. 77–88.
Generic unfoldings and normal forms of some singularities arising in the obstacle problem, Duke Math. Jour. 46 (1979), 645–683.
The parametrized obstacle problem (with S.-N. Chow), J. Nonlinear Anal. 4 (1980), 73–91.
Generic bifurcation in the obstacle problem, Quart. Appl. Math. (1980), 355-387.
An example of bifurcation to homoclinic orbits (with S.-N. Chow and J.K. Hale),
J. Differential Equations 37 (1980), 351–373.
Snakes: oriented families of periodic orbits, their sources, sinks and continuation (with J.A. Yorke), J. Differential Equations 43 (1982), 419–450.
Families of periodic orbits: local continuability does to imply global continuability (with K.T. Alligood and J.A. Yorke), J. Differential Geometry 16 (1981), 483–492.
A periodic orbit index which is a bifurcation invariant (with S.-N. Chow and J.A. Yorke), Geometric Dynamics, Springer–Verlag Lecture Notes in Mathematics, Vol. 1007 (1983), 109–131.
An index for the global continuation of relatively isolated sets of periodic orbits (with K.T.
Alligood and J.A. Yorke), Geometric Dynamics, Springer–Verlag Lecture Notes in Mathematics, Vol. 1007 (1983), 1–21.
Regularity results for real analytic homotopies (with T.Y. Li and J.A. Yorke), Numerische Mathematik, 46 (1985), 43–50.
The Lyapunov dimension of a nowhere differentiable attracting torus (with J.A. Kaplan and J.A. Yorke), Ergodic Theory and Dynamical Systems 4 (1984), 261–281.
Morse decompositions and global continuation of periodic solutions of singularly perturbed delay equations, in Systems of Nonlinear Partial Differential Equations (ed. by J.M. Ball), pp. 351–365, D. Reidel, Dordrecht, 1983.
Singularly perturbed delay-differential equations (with S.-N. Chow) in Coupled Nonlinear Oscillators (ed. by J. Chandra and A.C. Scott), North Holland Math. Studies 80 (1983), 7–12.
Stable transition layers in a semilinear boundary value problem (with S.B. Angenent and L. A. Peletier), J. Differential Equations 67 (1987), 212–242.
Stability, multiplicity and global continuation of symmetric periodic solutions of a nonlinear Volterra integral equation (with S.-N. Chow and O. Diekmann), Jap. Jour. Appl. Math. 2 (1985), 433–469.
Global continuation and asymptotic behavior for periodic solutions of a differential–delay equation (with R.D. Nussbaum), Ann. Mat. Pura ed Applicata 145 (1986), 33–128.
A bifurcation gap for a singularly perturbed delay equation (with R. D. Nussbaum), in Chaotic Dynamics and Fractals (ed. by M.F. Barnsley and S.G. Demko), pp. 263–286, Academic Press, 1986.
Hopf bifurcation and symmetry: traveling and standing waves on the circle (with S. van Gils), Proc. Roy. Soc. Edinburgh 104A (1986), 279–307.
Switchings of optimal controls and the equation y (4) + |y|_ sign y = 0, 0 < _ < 1 (with P. Brunovsky), Casopis pro Pestivani Matematiky 110 (1985), 302–313.
Lorenz–like chaos in a partial differential equation for a heated fluid loop (with J.A. Yorke and E.D. Yorke), Physica 24D (1987), 279–291.
Morse decompositions for delay–differential equations, J. Differential Equations 72 (1988) 270–315.
The principle of spatial averaging and inertial manifolds for reaction–diffusion equations (with G.R. Sell), in Nonlinear Semigroups, Partial Differential Equations and Attractors, Springer–Verlag Lecture Notes in Mathematics, Vol. 1248 (1987), 94–107.
Inertial manifolds for reaction–diffusion equations in higher space dimensions (with G.R. Sell), Jour. Amer. Math. Soc. 1 (1988), 805–866.
Transition layers for singularly perturbed delay differential equations with monotone nonlinearities
(with S.-N. Chow and X.-B. Lin), Jour. Dyn. Diff. Eq. 1 (1989), 3–43.
Connections between Morse sets for delay–differential equations (with B. Fiedler), Jour. Reine Ang. Mat. 397 (1989), 23–41.
The Poincare–Bendixson theorem for scalar reaction diffusion equations (with B. Fiedler), Arch. Rat. Mech. Anal. 107 (1989), 325–345.
The Poincare–Bendixson theorem for monotone cyclic feedback systems (with H.L. Smith), J. Dyn. Diff. Eq. 2 (1990), 367–421.
A differential–delay equation arising in optics and physiology (with R.D. Nussbaum), SIAM Jour. Math. Anal. 20 (1989), 249–292.
Multiple transition layers in a singularly perturbed differential–delay equation (with R.D. Nussbaum), Proc. Roy. Soc. Edinburgh 123A (1993), 1119–1134.
Stable periodic solutions for the hypercycle system (with J. Hofbauer and H. L. Smith), J. Dyn. Diff. Eq. 3 (1991), 423–436.
Ponies on a merry-go-round in large arrays of Josephson junctions (with D. G. Aronson and M. Golubitsky), Nonlinearity 4 (1991), 903–910.
Floquet theory for parabolic differential equations: (with S.-N. Chow and K. Lu), J.
Differential Equations 109 (1994), 147–200.
Boundary layer phenomena for differential delay equations with state dependent time lags, I (with R. D. Nussbaum), Arch. Rat. Mech. Anal. 120 (1992), 99–146.
Obstructions to the existence of normally hyperbolic inertial manifolds (with G. R. Sell and Z. Shao), Indiana Univ. Math. J. 42 (1993), 1027–1055.
Periodic solutions for functional differential equations with multiple state-dependent time lags (with R. D. Nussbaum and P. Paraskevopoulos), Top. Meth. Nonlin. Anal. 3 (1994), 101–162.
Boundary layer phenomena for differential delay equations with state dependent time lags, II (with R. D. Nussbaum), J. Reine Angew. Math. 477 (1996), 129–197.
Floquet bundles for scalar parabolic equations (with S.-N. Chow and K. Lu), Arch. Rat. Mech. Anal., 129 (1995), 245–304.
Pattern formation and spatial chaos in lattice dynamical systems, I, (with S.-N. Chow) IEEE Trans. Circuits Syst. 42 (1995), 746–751.
Pattern formation and spatial chaos in lattice dynamical systems, II, (with S.-N. Chow) IEEE Trans. Circuits Syst. 42 (1995), 752–756.
Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions (with G.R. Sell), J. Diff. Eq. 125 (1996), 385–440.
The Poincaré–Bendixson theorem for monotone cyclic feedback systems with delay (with G.R.Sell), J. Diff. Eq., 125 (1996), 441–489.
Stability and oscillation in nonlinear cyclic systems, in: Differential Equations and Applications to
Biology and Industry (eds. M. Martelli, K. Cooke, E. Cumberbatch, B. Tang, and H. Thieme),
World Scientific Publishers, Singapore, 1996, pp. 337–346.
Dynamics of lattice differential equations (with S.-N. Chow and E. Van Vleck), Int. J. Bifurcation and Chaos 6 (1996), pp. 1605–1621.
Pattern formation and spatial chaos in spatially discrete evolution equations (with S.-N. Chow and E. Van Vleck), Random & Computational Dynamics 4 (1996), 109–178.
Spatial patterns, spatial chaos, and traveling waves in lattice differential equations, in:
Stochastic and Spatial Structures of Dynamical Systems (eds. S.J. van Strien and S.M. Verduyn Lunel), North-Holland, Amsterdam, 1996, pp. 105–129.
Recent progress in lattice dynamical systems (with S.-N. Chow), Japanese Society for Industrial and Applied Mathematics, accepted for publication.
Traveling waves in lattice dynamical systems, (with S.-N. Chow and W. Shen), J. Diff. Eq.149 (1998), pp. 248–291.
Modeling reflex asymmetries with implicit delay differential equations (with F.M. Atay), Bull. Math. Biol. 60 (1998), pp. 999–1015.
Traveling wave solutions for systems of ODE’s on a two-dimensional spatial lattice (with J. W. Cahn and E. Van Vleck), SIAM J. Appl. Math. 59 (1999), pp. 455–493.
The Fredholm alternative for functional differential equations of mixed type, J. Dyn. Diff. Eq. 11 (1999), pp. 1–47.
The global structure of traveling waves in spatially discrete systems, J. Dyn. Diff. Eq. 11 (1999), pp. 49–127.
Crystallographic pinning: direction dependent pinning in lattice differential equations, J. Diff. Eq., to appear (91 pages).
Exponential dichotomies and Wiener-Hopf factorizations for mixed-type functional differential equations via holomorphic factorization (with S. Verduyn Lunel), J. Diff. Eq., to appear (81 pages).
Eigenvalues for a class of homogeneous cone maps arising from max-plus operators (with R.D. Nussbaum), Disc. Conts. Dyn. Syst. 8 (2002), pp. 519–562.
A basis theorem for a class of max-plus eigenproblems (with R.D. Nussbaum), J. Diff. Eq.189 (2003), pp. 616–639.
Boundary layer phenomena for delay-differential equations with state dependent time lags: III (with R.D. Nussbaum), J. Diff. Eq. 189 (2003), pp. 640–692.
Theorems of Hartman-Grobman type for singularly perturbed vector fields (with S.-N. Chow and P. Brunovský), Trans. Amer. Math. Soc., to appear (58 pages).
Traveling waves in spatially discrete systems, in: Dynamical Systems, Cetraro, Italy, 2000 (eds. J.W. Macki and P. Zecca), Springer–Verlag Lecture Notes in Mathematics, Vol. 1822 (2003), pp. 231–298.
Differential systems with feedback: time discretizations and Lyapunov functions (with G.R. Sell), Disc. Conts. Dyn. Syst. 15 (2003), pp. 659–698.
Universality of Crystallographic Pinning (with A. Hoffman), preprint.
Inequivalent Measures of Noncompactness (with R.D. Nussbaum), preprint.
Superstability and rigorous asymptotics in singularly perturbed differential equations with state-dependent delays (with R.D. Nussbaum), preprint.
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