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Book Review

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Book Information:

Author: A. M. Fink
Title: Almost periodic differential equations
Additional book information: Lecture Notes in Mathematics, No. 377. Springer-Verlag, Berlin, Heidelberg, New York, 1974, vii+336 pp.

Authors: R. Reissig, G. Sansone and R. Conti
Title: Nonlinear differential equations of higher order
Additional book information: Noordhoff, Leyden, 1974, xiii+669 pp.

Author: J. K. Hale
Title: Functional differential equations
Additional book information: Applied Mathematical Sciences, No. 3. Springer-Verlag, New York, Heidelberg, Berlin, 1971, viii+238 pp.

References [Enhancements On Off] (What's this?)

  • 1. V. I. Arnol'd, Proof of a theorem of A. N. Kolmogorov on the preservation of quasiperiodic motions under a small perturbation of the Hamiltonian, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 13-40 = Russian Math. Surveys 18 (1963), no. 5, 9-36. MR 29 #328. MR 163025
  • 2. R. E. Bellman and K. L. Cooke, Differential-differénce equations, Academic Press, New York, 1963. MR 26 #5259; erratum, 27, p. 1399. MR 146481
  • 3. G. D. Birkhoff, Collected mathematical papers. Vol. 1, Amer. Math. Soc. Providence, R. I., 1950; reprint, Dover, New York, 1968, pp. 654-751; Vol. 2, pp. 111-229, 283-332, 530-661. MR 38 #4271a, b.
  • 4. G. D. Birkhoff, Collected mathematical papers. Vol. 2, Amer. Math. Soc., Providence, R.I., 1950; reprint, Dover, New York, 1968, pp. 295-332, 360-394, 398-408, 462-465, 713-717. MR 38 #427 1b.
  • 5. G. D. Birkhoff, Collected mathematical papers. Vol. 2, Amer. Math. Soc. Providence, R.I., 1950; reprint, Dover, New York, 1968, pp. 710-712. MR 38 #4271b.
  • 6. G. D. Birkhoff, Collected mathematical papers. Vol. 2, Amer. Math. Soc. Providence, R.I., 1950; reprint, Dover, New York, 1968, pp. 295-332. MR 38 #4271b.
  • 7. S. Bochner, Beiträge zur Theorie der fastperiodischen Funktionen, Math. Ann. 96 (1927), no. 1, 119–147 (German). MR 1512308, https://doi.org/10.1007/BF01209156
  • 8. S. Bochner, A new approach to almost periodicity, Proc Nat. Acad. Sci. U.S.A. 48 (1962), 2039-2043. MR 26 #2816. MR 145283
  • 9. Harald Bohr, Zur Theorie der fastperiodischen Funktionen, Acta Math. 47 (1926), no. 3, 237–281 (German). III. Dirichletentwicklung analytischer Funktionen. MR 1555216, https://doi.org/10.1007/BF02543846
  • 10. M. L. Cartwright, Almost periodic flows and solutions of differential equations, Proc. London Math. Soc (3) 17 (1967), 355-380; corrigenda, ibid. (3) 17 (1967), 768. MR 36 #6697. MR 223649
  • 11. M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167-181. MR 39 #548. MR 239191
  • 12. L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete; N.F., Heft 16, Springer-Verlag, Berlin, 1959. MR 22 #9673. MR 118904
  • 13. J. Favard, Leçons sur les fonctions presque-périodiques, Gauthier-Villars, Paris, 1933.
  • 14. Philip Franklin, Almost periodic recurrent motions, Math. Z. 30 (1929), no. 1, 325–331. MR 1545065, https://doi.org/10.1007/BF01187774
  • 15. W. Hahn, Stability of motion, Die Grundlehren der math. Wissenschaften, Band 138, Springer-Verlag, New York, 1967. MR 36 #6716. MR 223668
  • 16. E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vols. I, II, Die Grundlehren der math. Wissenschaften, Bände 115, 152, Academic Press, New York; Springer-Verlag, Berlin, 1963, 1970. MR 28 #158; 41 #7378; erratum, 42, p. 1825. MR 262773
  • 17. E. L. Ince, Ordinary differential equations, Dover, New York, 1956. MR 6, 65. MR 10757
  • 18. A. N. Kolmogorov, On conservation of quasi-periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk SSSR 98 (1954), 527-530. (Russian) MR 16, 924. MR 68687
  • 19. E. R. van Kampen, Almost periodic functions and compact groups, Ann. of Math. (2) 37 (1936), no. 1, 78–91. MR 1503270, https://doi.org/10.2307/1968688
  • 20. J. P. LaSalle and S. Lefschetz, Stability by Liapunov's direct method, with applications, Math. in Sci. and Engineering, vol. 4, Academic Press, New York, 1961. MR 24 #A2712.
  • 21. W. Maak, Fastperiodische Funktionen, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 61, Springer-Verlag, Berlin and New York, 1967. MR 35 #5860. MR 215015
  • 22. R. K. Miller and G. R. Sell, Topological dynamics and its relation to integral equations and nonautonomous systems, Proc Conf. on Dynamical Systems, Providence, August, 1974 (to appear). MR 650822
  • 23. J. K. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136-176. MR 34 #7888. MR 208078
  • 24. V. V. Nemyckiĭ and V. V. Stepanov, Qualitative theory of differential equations, OGIZ, Moscow, 1947; English transl., Princeton Math. Ser., no. 22, Princeton Univ. Press, Princeton, N.J., 1960. MR 10, 612; 22 #12258. MR 29483
  • 25. J. v. Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445–492. MR 1501752, https://doi.org/10.1090/S0002-9947-1934-1501752-3
  • 26. L. S. Pontrjagin, Continuous groups, GITTL, Moscow, 1938; English transl., Topological groups, Princeton Math. Ser., no. 2, Princeton Univ. Press, Princeton, N.J., 1939. MR 1, 44.
  • 27. R. Reissig, G. Sansone and R. Conti, Qualitative Theorie nichtlinearer Differentialgleichungen, Edizioni Cremonese, Rome, 1963. MR 28 #1347. MR 158121
  • 28. G. R. Sell, Topological dynamics and ordinary differential equations, Van Nostrand Reinhold, London, 1971. MR 442908
  • 29. G. R. Sell, Topological dynamical techniques for differential and integral equations, Ordinary Differental Equations, Academic Press, New York, 1972, pp. 287-304. MR 419902

Review Information:

Reviewer: George R. Sell
Journal: Bull. Amer. Math. Soc. 82 (1976), 198-207
DOI: https://doi.org/10.1090/S0002-9904-1976-13985-7
American Mathematical Society