Publications

0. Dissertation: "On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations",Courant institute of Mathematical Sciences, New York Univ, IMM-NYU 333, 1964

1. "A new approach to the perturbation theory in invariant surfaces," Comm. Pure Appl. Math. 18(1965), 717-732.

2. "A perturbation theorem for invariant Riemannian manifolds." Differential equations and dynamical systems

(Proc. 1965 Puerto Rico Symposium), Academic Press, 1967 43-54.

3. "A perturbation theorem for invariant manifolds and holder continuity," J. Math. & Mech. 18(1969), 706-762.

4. "The existence of periodic solutions on two-manifolds," (with G. Sell). SIAM

Studies Appl. Math. No. 5 1969, 117-118.

5. "The homology of invariant sets of flows," Ordinary Differential Equations,

Academic press, 1972, 265-275.
6. "On the existence of nontrivial recurrent motions," (with G. Sell). J. Differential
Equations, 11(1972), 449-463.
7. "On the existence of nontrivial recurrent motions," (with G. Sell). Duke Math. J.
40(1973), 815-819.
8. "Asymptotic approach to periodic orbits," Tech. Rep. 1972/9, Istituto "U. Dini,"
Firenze, 1972.
9. "Asymptotic approach to periodic orbits and local prolongations of maps."
Pacific J. Math. 51(1974), 273-287.
10. "Skew-product flows, finite extensions of minimal transformation groups and
almost periodic differential equations," (with G. Sell). Bull. Amer. Math. Soc. 79(1973), 802-805.
11. "Finite extensions of minimal transformation groups," (with G. Sell). Trans.
Amer. Math. Soc. 190(1974), 325-334.
12. "Existence of dichotomies and invariant splittings for linear differential systems I,"
(with G. Sell). J. Differential Equations. 15(1974), 429-458.
13. "A note on Anosov diffeomorphisms," (with G. Sell). Bull. Amer. Math. Soc.
80(1974), 278-280.
14. "A note on almost periodic differential equations," (with G. Sell). Equations Diff.
Fonctionelles Non lin. (Actes Conf. "Equa-Diff. 73") Bruxelles et Louvain-La- Neuve 1973, 93-96.
15. "Existence of dichotomies and invariant splittings for linear differential systems II,"

(with G. Sell). J. Differential Equations 22(1976), 478-496

16. " Skew-product dynamical systems," in Dynamical Systems, Vol. 2, Academic Press 1976, 175-179.

17. "A spectral theory for linear almost periodic differential equations". (with G. Sell).

Proc. Internat. Conf. on Differential Equations (Los Angeles 1974), 698-708. Academic Press, 1975.
18. "Linear skew-product dynamical systems," Proc. 3rd. Mexico-U. S. A. Symposium, in
"Ecuaciones Differenciales" by Carlos Imaz.(1976)
19. "Existence of dichotomies and invariant splittings for linear differential systems III,"
(with G. Sell). J. Differential Equations 22 (1976), 497-522.
20. "Lifting properties in skew-product flows with applications to Differential
Equations," (with G. Sell). AMS Memoirs Vol. 11 No. 190 July 1977.
21. "A Spectral Theory for Linear Differential Systems," (with G. Sell). J. Differential
Equations Vol. 27 No. 3(1978),. 320-358.
22. "Existence of dichotomies and invariant splittings for linear differential systems IV."
J. Differential Equations Vol. 27 No. 1(1978), 106-137.
23. "The Splitting Index for Linear Differential Systems," J. Differential Equations,
J. Differential Eq. Vol. 33 No. 3(1979), 368-405.
24. "Stability and Asymptotic Integration for Certain Linear Systems of Functional
Differential Equations," (with J. R. Haddock), J. Math. Anal. and Appl. Vol. 76 No. 2(1980), 328-338.
25. "Singular Perturbations and Conditional Stability," (with G. Sell). J. Math. Anal.
and Appl. Vol. 76 No. 2(1980), 406-431.
26. "The Spectrum of an Invariant Submanifold," J. Differential Eq. Vol. 38 No.
22(1980), 135-160 (with G. Sell).
27. "Exponential Dichotomies in Evolutionary Equations," (with G. Sell). Volterra
and Functional Differential Equation Vol. 81(1982), 167-174.
28. "Dichotomies for Linear Evolutionary Equations in Banach Space,"(Joint with G.

Sell), J. Differential Eq. 113(1994), 17-67(Selected by American Mathematical

Society for Featured Review)

29. "A new approach to asymptotic diagonalization of linear differential systyems,"

(with Sigrun Bodine) J. Dynamics and Differential Equations, Vol. 12,1, 2000, 229-245

30. "Asymptotic diagonalization of linear difference equations"(with Sigrun Bodine)

Journal of Difference Equations and Applications, 2001, Vol. 7, 637-650

31."Bifurcation of maps and cycling in genetic systems" (with Hubertus F. von Bremen)

Fields Institute Comm. Vol 42, 2004, 305-311

32. "Open problems on cycling in genetic systems" Fields Institute Comm. Vol 42, 2004, 535-436

33. "A new approach to cycling in a 2-locus 2-allele genetic model" (with Hubertus F.von Bremen)

J. Difference Eq. and Appl.9(5) May 2003, 441-448

33a -Corrigendum- A new approach to cycling ..(#32) J. Difference Eq. and Appl.9(9) Sept. 2003, p. 868

34. "Global stability of periodic orbits of nonautonomous difference equations and population biology"

(with Saber Elaydi) J. Differential Eq. 208(1)2005, 258-273

35. "Global stability of periodic orbits of nonautonomous difference equations in population biology

and the Cushing-Henson conjectures", Proceedings of 8th International Conference on Difference Equations and Applications Brno, Czech Republic (with Saber Elaydi). Elaydi, et.al. editors, Chapman and Hall, 2005, .113-126

36. "Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures" (with S. Elaydi)

J. Difference Eq. and Appl. 11, Nos. 4-5, 2005, 337-346

37. "Basin of attraction of periodic orbits of maps on the real line" J. Difference Eq.and Appl.

(with S. Elaydi) V.10 No.10, August 2004, 881-888

38. "Periodic difference equations, population biology and the Cushing-Henson conjectures"

(with S. Elaydi) Math. Biosciences, 201(2006) 195-207

39. "Skew-product dynamical systems: Applications to difference equations"

Proceedings of the Second Annual Celebration of Mathematics, United Arab Emirates (2005) (with Saber Elaydi). (to appear)

40. "Global asymptotic stability in the Jia Li model for genetically altered mosquitos" (with H. von Bremen)

Proceedings of 9th International Conference on Difference Equations and Applications, Los Angeles(2004),World Scientific 2005, 87-100.

41. "The stochastic Beverton-Holt equation and the M. Neubert conjecture" (with Cymra Haskell)

J. Dynamics and Differential Equations, 17, No.4, 2005, 825-844

42. "Some Stability Results in a Model for Genetically Altered Mosquitoes" (with H. von Bremen), Modeling and Control of Autonomous Decision Support Based Systems, Shaker Verlag, 2005. pp. 301-308.

43. "A Note on Periodic Ricker Maps" J. Difference Eq. & Appl., 13, No. 1, January 2007, 89-92.

44. "Dynamic Reduction with applications to Mathematical Biology and other areas" (with H. von Bremen) J. Biological Dynamics,1(4), October 2007, 437-453

 

45. Introduction to the 2009 Re-Publication of the "Neimark-Sacker Bifurcation Theorem", J. Difference Eq. and Appl., 15 (8-9) 2009, 753-758

45a. "Chapter 2 of Author's 1964 Dissertation", J. Difference Eq. and Appl., 15(8-9) 2009, 759-774 (see Publication "0" above for full dissertation)

45b. "Erratum". Publication error in 45a (above), J. Difference Eq. and Appl. 15(10) 2009, 1027

 

46. "Semigroups of Maps and Periodic Difference Equation", J. Difference Eq. and Appl., 16(1), January 2010, 1-13

47. "Population models with Allee effect: A new model", (with Saber Elaydi) J. Biological Dynamics, 4(4) July 2010, 397-408

48. "A Conjecture on the Stability of the Periodic Solutions of Ricker's Equation With Periodic Parameters", Applied Mathematics and Computation, 217 (2010) 1213-1219

49. "A Note: An Invariance Theorem for Mappings", J. of Difference Eq. and Appl., 18(1) 2012, 163-166

50. "Global Stability in a multi-species periodic Leslie-Gower model", J. Biological Dynamics 5(5) 2011, 549-562