{"id":187,"date":"2023-06-15T15:23:07","date_gmt":"2023-06-15T22:23:07","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/robert-sacker\/?page_id=187"},"modified":"2023-06-21T11:17:19","modified_gmt":"2023-06-21T18:17:19","slug":"publications","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/robert-sacker\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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1. “A new approach to the perturbation theory in invariant surfaces,” Comm. Pure Appl. Math.\u00a018(1965), 717-732.<\/p>\n

2. “A perturbation theorem for invariant Riemannian manifolds.” Differential equations and dynamical systems (Proc. 1965 Puerto Rico Symposium), Academic Press, 1967 43-54.<\/p>\n

3. “A perturbation theorem for invariant manifolds and holder continuity,” J. Math. & Mech.\u00a018(1969), 706-762.<\/p>\n

4. “The existence of periodic solutions on two-manifolds,” (with G. Sell).\u00a0SIAM\u00a0Studies Appl. Math. No. 5 1969, 117-118.<\/p>\n

5. “The homology of invariant sets of flows,” Ordinary Differential Equations, Academic press, 1972, 265-275.<\/p>\n

6. “On the existence of nontrivial recurrent motions,” (with G. Sell). J. Differential Equations,\u00a011(1972), 449-463.<\/p>\n

7. “On the existence of nontrivial recurrent motions,” (with G. Sell). Duke Math. J. 40(1973), 815-819.<\/p>\n

8. “Asymptotic approach to periodic orbits,” Tech. Rep. 1972\/9, Istituto “U. Dini,” Firenze, 1972.<\/p>\n

9. “Asymptotic approach to periodic orbits and local prolongations of maps.” Pacific J. Math.51(1974), 273-287.<\/p>\n

10. “Skew-product flows, finite extensions of minimal transformation groups and almost periodic differential equations,” (with G. Sell). Bull. Amer. Math. Soc.\u00a079(1973), 802-805.<\/p>\n

11. “Finite extensions of minimal transformation groups,” (with G. Sell). Trans. Amer. Math. Soc.\u00a0190(1974), 325-334.<\/p>\n

12. “Existence of dichotomies and invariant splittings for linear differential systems I,” (with G. Sell). J. Differential Equations.\u00a015(1974), 429-458.<\/p>\n

13. “A note on Anosov diffeomorphisms,” (with G. Sell). Bull. Amer. Math. Soc.80(1974), 278-280.<\/p>\n

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.<\/p>\n

15. “Existence of dichotomies and invariant splittings for linear differential systems II,”(with G. Sell). J. Differential Equations 22(1976), 478-496<\/p>\n

16. ” Skew-product dynamical systems,” in Dynamical Systems, Vol. 2, Academic Press 1976, 175-179.<\/p>\n

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.<\/p>\n

18. “Linear skew-product dynamical systems,” Proc. 3rd. Mexico-U. S. A. Symposium, in “Ecuaciones Differenciales” by Carlos Imaz.(1976)<\/p>\n

19. “Existence of dichotomies and invariant splittings for linear differential systems III,” (with G. Sell). J. Differential Equations\u00a022\u00a0(1976), 497-522.<\/p>\n

20. “Lifting properties in skew-product flows with applications to Differential Equations,” (with G. Sell). AMS Memoirs Vol. 11 No. 190 July 1977.<\/p>\n

21. “A Spectral Theory for Linear Differential Systems,” (with G. Sell). J. Differential Equations Vol. 27 No. 3(1978),. 320-358.<\/p>\n

22. “Existence of dichotomies and invariant splittings for linear differential systems IV.”J. Differential Equations Vol. 27 No. 1(1978), 106-137.<\/p>\n

23. “The Splitting Index for Linear Differential Systems,” J. Differential Equations, J. Differential Eq. Vol. 33 No. 3(1979), 368-405.<\/p>\n

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.<\/p>\n

25. “Singular Perturbations and Conditional Stability,” (with G. Sell). J. Math. Anal. and Appl. Vol. 76 No. 2(1980), 406-431.<\/p>\n

26. “The Spectrum of an Invariant Submanifold,” J. Differential Eq. Vol. 38 No. 22(1980), 135-160 (with G. Sell).<\/p>\n

27. “Exponential Dichotomies in Evolutionary Equations,” (with G. Sell). Volterra and Functional Differential Equation Vol. 81(1982), 167-174.<\/p>\n

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)<\/p>\n

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<\/p>\n

30. “Asymptotic diagonalization of linear difference equations”(with Sigrun Bodine) Journal of Difference Equations and Applications, 2001, Vol. 7, 637-650<\/p>\n

31.”Bifurcation of maps and cycling in genetic systems” (with Hubertus F. von Bremen)\u00a0Fields Institute Comm. Vol 42, 2004, 305-311<\/p>\n

32. “Open problems on cycling in genetic systems”\u00a0Fields Institute Comm. Vol 42, 2004, 535-436<\/p>\n

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<\/p>\n

33a\u00a0Corrigendum- A new approach to cycling ..(#32)<\/a>\u00a0J. Difference Eq. and Appl.9(9) Sept. 2003, p. 868<\/p>\n

34. “Global stability of periodic orbits of nonautonomous difference equations and population biology” (with Saber Elaydi) J. Differential Eq. 208(1)2005, 258-273<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

38. “Periodic difference equations, population biology and the Cushing-Henson conjectures” (with S. Elaydi) Math. Biosciences, 201(2006) 195-207<\/p>\n

39.\u00a0“Skew-product dynamical systems: Applications to difference equations”<\/a>\u00a0Proceedings of the Second Annual Celebration of Mathematics, United Arab Emirates (2005) (with Saber Elaydi). (to appear)<\/p>\n

40.\u00a0“Global asymptotic stability in the Jia Li model for genetically altered mosquitos” (with H. von Bremen)<\/a>\u00a0Proceedings of 9th International Conference on Difference Equations and Applications, Los Angeles(2004),World Scientific 2005, 87-100.<\/p>\n

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<\/p>\n

42.\u00a0“Some Stability Results in a Model for Genetically Altered Mosquitoes”<\/a>\u00a0(with H. von Bremen), Modeling and Control of Autonomous Decision Support Based Systems, Shaker Verlag, 2005. pp. 301-308.<\/p>\n

43.\u00a0“A Note on Periodic Ricker Maps” J. Difference Eq. & Appl., 13, No. 1, January 2007, 89-92.<\/p>\n

44.\u00a0“Dynamic Reduction with applications to Mathematical Biology and other areas”<\/a>\u00a0(with H. von Bremen) J. Biological Dynamics,1(4), October 2007, 437-453<\/p>\n

45.\u00a0Introduction to the 2009 Re-Publication of the\u00a0“Neimark-Sacker Bifurcation Theorem”<\/a>, J. Difference Eq. and Appl., 15 (8-9) 2009, 753-758<\/p>\n

45a.\u00a0“Chapter 2 of Author’s 1964 Dissertation<\/a>“, J. Difference Eq. and Appl., 15(8-9) 2009, 759-774\u00a0(see Publication “0” above for full dissertation)<\/p>\n

45b.\u00a0“Erratum<\/a>“. Publication error in 45a (above), J. Difference Eq. and Appl. 15(10) 2009, 1027<\/p>\n

46.\u00a0“Semigroups of Maps and Periodic Difference Equation”<\/a>, J. Difference Eq. and Appl., 16(1), January 2010, 1-13<\/p>\n

47.\u00a0“Population models with Allee effect: A new model”<\/a>, (with Saber Elaydi) J. Biological Dynamics, 4(4) July 2010, 397-408<\/p>\n

48. “A Conjecture on the Stability of the Periodic Solutions of Ricker’s Equation With Periodic Parameters<\/a>“, Applied Mathematics and Computation, 217 (2010) 1213-1219<\/p>\n

49. “A Note: An Invariance Theorem for Mappings<\/a>“, J. of Difference Eq. and Appl., 18(1) 2012, 163-166<\/p>\n

50. “Global Stability in a multi-species periodic Leslie-Gower model<\/a>“, J. Biological Dynamics 5(5) 2011, 549-562<\/p>\n

51.\u00a0Difference Equations with the Allee Effect and the Periodic Sigmoid Beverton- Holt Equation<\/a>, J. Biological Dynamics, (with G. Gaut, K. Goldring, F. Grogan, C. Haskell) 6(2)2012, pp. 1019-1033<\/p>\n

52.\u00a0A Note:\u00a0An Invariance Theorem for Mappings II<\/a>, J. Dynamics and Diferential Equations, 24(3)2012, pp. 595-599<\/p>\n

53.\u00a0Resonance and Attenuation in the n-periodic Beverton-Holt Equation<\/a>, (with Yi Yang), J. Difference Equ. and Appl.19(7) 2013, 1174-1191<\/p>\n

54.\u00a0Periodic Unimodal Allee Maps, the Semigroup Property and the Lambda-Ricker Map with Allee Effect<\/a>\u00a0(with Yi Yang) Discrete and Continuous Dynam. Syst.-B, 19(2) March 2014, 589-606<\/p>\n

55.\u00a0On a Discrete Selection-Mutation Model\u00a0<\/a>(with Azmy Ackleh and Paul Salceanu) J. Difference Equ. and Appl. 20(10), October 2014, 1383-1403<\/p>\n

56.\u00a0Global Stability in the 2D Ricker Equation<\/a>\u00a0(with Brian Ryals) J. Difference Equ. and Appl. 21(11)\u00a02015, 1068-1081<\/p>\n

57. Global Stability in the 2D Ricker Equation-Revisited (with Brian Ryals) Discrete and Continuous Dynam. Syst. -B, 22(2) 2017, pp. 585-604<\/p>\n

58. Almost Periodicity, Ricker Map, Beverton-Holt Map and Others, a General Method, J. Differernce Equations and Appl.,23(7) 2017, 1286-1297<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":370,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-187","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nPublications - Robert Sacker<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/robert-sacker\/publications\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Publications - Robert Sacker\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/robert-sacker\/publications\/\" \/>\n<meta property=\"og:site_name\" content=\"Robert Sacker\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-21T18:17:19+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/robert-sacker\/publications\/\",\"url\":\"https:\/\/dornsife.usc.edu\/robert-sacker\/publications\/\",\"name\":\"Publications - 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