Bulletin of the American Mathematical Society

MathSciNet review: 1567490
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Book Information:

Authors: B. M. Levitan and V. V. Zhikov
Title: Almost periodic functions and differential equations
Additional book information: Cambridge University Press, New York, 1983, x + 211 pp., $34.50. ISBN 0-5212-4407-2.

1.

H. Bohr and O. Neugebauer, Über lineare Differentialgleichungen mit konstanten Koeffizienten und Fastperiodischer recter Seite, Nachr. Ges. Wiss. Gottingen, Math.-Phys. Klasse, 1926, pp. 8-22.

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

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

R. K. Miller, Almost periodic differential equations as dynamical systems with applications to the existence of A.P. solutions, J. Differential Equations 1 (1965), 337–345. MR 185221, DOI 10.1016/0022-0396(65)90012-4

V. M. Millionščikov, Recurrent and almost periodic limit trajectories of non-autonomous systems of differential equations, Dokl. Akad. Nauk SSSR 161 (1965), 43–44 (Russian). MR 0173835

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

7.

J. Favard, Sur les équationes différentielles a coefficients presque-périodiques, Acta Math. 51 (1927), 95-112.

Luigi Amerio and Giovanni Prouse, Almost-periodic functions and functional equations, Van Nostrand Reinhold Co., New York-Toronto, Ont.-Melbourne, 1971. MR 0275061

Luigi Amerio, Soluzioni quasi-periodiche, o limitate, di sistemi diferenziali non lineari quasi-periodici, o limitati, Ann. Mat. Pura Appl. (4) 39 (1955), 97–119 (Italian). MR 79687, DOI 10.1007/BF02410765

T. Yoshizawa, Stability theory and the existence of periodic solutions and almost periodic solutions, Applied Mathematical Sciences, Vol. 14, Springer-Verlag, New York-Heidelberg, 1975. MR 0466797

Jürgen Moser, Stable and random motions in dynamical systems, Annals of Mathematics Studies, No. 77, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1973. With special emphasis on celestial mechanics; Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N. J. MR 0442980

Robert J. Sacker and George R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. III, J. Differential Equations 22 (1976), no. 2, 497–522. MR 440621, DOI 10.1016/0022-0396(76)90043-7

Russell A. Johnson, A linear, almost periodic equation with an almost automorphic solution, Proc. Amer. Math. Soc. 82 (1981), no. 2, 199–205. MR 609651, DOI 10.1090/S0002-9939-1981-0609651-0

14.

N. Bogolyubov, O nekotorykh statisticheskikh methodakh v matematicheskoĭ fizike (On some statistical methods in mathematical physics), Akad. Nauk Ukrainskoĭ SSR, 1945.

1.

H. Bohr and O. Neugebauer, Über lineare Differentialgleichungen mit konstanten Koeffizienten und Fastperiodischer recter Seite, Nachr. Ges. Wiss. Gottingen, Math.-Phys. Klasse, 1926, pp. 8-22.

2.

S. Bochner, A new approach to almost periodicity, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 2039-2043. MR 0145283

3.

S. Bochner, Beiträge zu theorie der Fastperiodischer Funktioner. I, Math. Ann. 96 (1927), 119-147. MR 1512308

4.

R. K. Miller, Almost periodic differential equations as dynamical systems with applications to the existence of almost periodic solutions, J. Differential Equations 1 (1965), 337-345. MR 185221

5.

V. M. Millionshchikov, Recurrent and almost periodic trajectories of nonautonomous systems of differential equations, Dokl. Akad. Nauk SSSR 161 (1965), 43-45; English transl., Soviet Math. Dokl. 7, 534-538. MR 173835

6.

G. Sell, Lectures on topological dynamics and differential equations, Van Nostrand Reinhold, London, 1971. MR 442908

7.

J. Favard, Sur les équationes différentielles a coefficients presque-périodiques, Acta Math. 51 (1927), 95-112.

8.

L. Amerio and G. Prouse, Almost periodic functions and functional equations, Van Nostrand, New York, 1955. MR 275061

9.

L. Amerio, Soluzioni quasi-periodiche, o limitate, di sistemi differenzali non lineari quasiperiodiche, o limitate, Ann. Mat. Pura Appl. (4) 39 (1955), 97-119. MR 79687

10.

T. Yoshizawa, Staiblity theory and the existence of periodic solutions and almost periodic solutions, Appl. Math. Sci., vol. 14, Springer-Verlag, New York, 1975. MR 466797

11.

J. Moser, Stable and random notions in dynamical systems, Ann. of Math. Studies, no. 77, Princeton Univ. Press, Princeton, N.J., 1973. MR 442980

12.

G. Sell and R. Sacker, Existence of dichotomies and invariant splittings for linear differential systems. III, J. Differential Equations 22 (1976), 497-522. MR 440621

13.

R. Johnson, A linear almost periodic equation with an almost automorphic solution, Proc. Amer. Math. Soc. 82 (1981), 199-205. MR 609651

14.

N. Bogolyubov, O nekotorykh statisticheskikh methodakh v matematicheskoĭ fizike (On some statistical methods in mathematical physics), Akad. Nauk Ukrainskoĭ SSR, 1945.