Bulletin of the American Mathematical Society

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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.

V. I. Arnol′d, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 13–40 (Russian). MR 0163025

Kenneth L. Cooke, Differential-difference equations, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 155–171. MR 0146481

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.

S. Bochner, Beiträge zur Theorie der fastperiodischen Funktionen, Math. Ann. 96 (1927), no. 1, 119–147 (German). MR 1512308, DOI 10.1007/BF01209156

S. Bochner, A new approach to almost periodicity, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 2039–2043. MR 145283, DOI 10.1073/pnas.48.12.2039

Harald Bohr, Zur Theorie der fastperiodischen Funktionen, Acta Math. 47 (1926), no. 3, 237–281 (German). III. Dirichletentwicklung analytischer Funktionen. MR 1555216, DOI 10.1007/BF02543846

M. L. Cartwright, Almost periodic flows and solutions of differential equations, Proc. London Math. Soc. (3) 17 (1967), 355–380; corrigenda, ibid. 17 (1967), 768. MR 223649, DOI 10.1112/plms/s3-17.4.768-s

M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167–181. MR 239191, DOI 10.1016/0022-0396(69)90110-7

Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 16, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959. MR 0118904

13.

J. Favard, Leçons sur les fonctions presque-périodiques, Gauthier-Villars, Paris, 1933.

Philip Franklin, Almost periodic recurrent motions, Math. Z. 30 (1929), no. 1, 325–331. MR 1545065, DOI 10.1007/BF01187774

Wolfgang Hahn, Stability of motion, Die Grundlehren der mathematischen Wissenschaften, Band 138, Springer-Verlag New York, Inc., New York, 1967. Translated from the German manuscript by Arne P. Baartz. MR 0223668

Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773

E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757

A. N. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton’s function, Dokl. Akad. Nauk SSSR (N.S.) 98 (1954), 527–530 (Russian). MR 0068687

E. R. van Kampen, Almost periodic functions and compact groups, Ann. of Math. (2) 37 (1936), no. 1, 78–91. MR 1503270, DOI 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.

W. Maak, Fastperiodische Funktionen, Die Grundlehren der mathematischen Wissenschaften, Band 61, Springer-Verlag, Berlin-New York, 1967 (German). Zweite, korrigierte Auflage. MR 0215015

Richard K. Miller and George R. Sell, Topological dynamics and its relation to integral equations and nonautonomous systems, Dynamical systems (Proc. Internat. Sympos., Brown Univ., Providence, R.I., 1974) Academic Press, New York, 1976, pp. 223–249. MR 0650822

Jürgen Moser, Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136–176. MR 208078, DOI 10.1007/BF01399536

V. V. Nemyckiĭ and V. V. Stepanov, Kačestvennaya Teoriya Differencial′nyh Uravneniĭ, OGIZ, Moscow-Leningrad, 1947 (Russian). MR 0029483

J. v. Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445–492. MR 1501752, DOI 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.

R. Reissig, G. Sansone, and R. Conti, Qualitative Theorie nichtlinearer Differentialgleichungen, Edizioni Cremonese, Rome, 1963 (German). MR 0158121

George R. Sell, Topological dynamics and ordinary differential equations, Van Nostrand Reinhold Mathematical Studies, No. 33, Van Nostrand Reinhold Co., London, 1971. MR 0442908

George R. Sell, Topological dynamical techniques for differential and integral equations, Ordinary differential equations (Proc. NRL-MRC Conf., Math. Res. Center, Naval Res. Lab., Washington, D.C., 1971) Academic Press, New York, 1972, pp. 287–304. MR 0419902

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 0163025

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. I, Math. Ann. 96 (1927), 119-147. MR 1512308

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.

H. Bohr, Zur Theorie der fastperiodischen Funktionen. I, II, III, Acta Math. 45 (1924), 29-127; 46 (1925), 101-214; 47 (1926), 237-281. MR 1555216

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.

P. Franklin, Almost periodic recurrent motions, Math. Z. 30 (1929), 325-331. MR 1545065

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. 37 (1936), 78-91. MR 1503270

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. von Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), 445-492. MR 1501752

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