Book Review
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MathSciNet review:
1568156
Full text of review:
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Book Information:
Author:
Jack K. Hale and Sjoerd M. Verduyn Lunel
Title:
Introduction to functional differential equations
Additional book information:
Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993, x + 447 pp., US$49.00. ISBN 0-387-94706-6.
Peter Dormayer, An attractivity region for characteristic multipliers of special symmetric solutions of $\dot x(t)=\alpha f(x(t-1))$ near critical amplitudes, J. Math. Anal. Appl. 169 (1992), no. 1, 70–91. MR 1180674, DOI 10.1016/0022-247X(92)90104-L
[H] G. E. Hutchinson, Circular causal systems in ecology, Ann. New York Acad. Sci., vol. 50, New York Acad. Sci., New York, 1948, pp. 221-246.
S. Kakutani and L. Markus, On the non-linear difference-differential equation $y^{\prime } (t)=[A-By(t-\tau )]y(t)$, Contributions to the theory of nonlinear oscillations, Vol. IV, Annals of Mathematics Studies, no. 41, Princeton University Press, Princeton, N.J., 1958, pp. 1–18. MR 0101953
Bernhard Lani-Wayda, Hyperbolic sets, shadowing and persistence for noninvertible mappings in Banach spaces, Pitman Research Notes in Mathematics Series, vol. 334, Longman, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1995. MR 1471208
[MS] J. Mallet-Paret and G. Sell, Systems of delay differential equations with discrete Lyapunov functions, preprint, Brown Univ., Providence, RI, 1993.
Roger D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of $x^{\prime } (t)=-g(x(t-1))$, J. Differential Equations 34 (1979), no. 1, 25–54. MR 549582, DOI 10.1016/0022-0396(79)90016-0
Russell A. Smith, Poincaré-Bendixson theory for certain retarded functional-differential equations, Differential Integral Equations 5 (1992), no. 1, 213–240. MR 1141738
Heinrich Steinlein and Hans-Otto Walther, Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for $C^1$-maps in Banach spaces, J. Dynam. Differential Equations 2 (1990), no. 3, 325–365. MR 1066620, DOI 10.1007/BF01048949
Hans-Otto Walther, Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations, Mem. Amer. Math. Soc. 79 (1989), no. 402, iv+104. MR 979430, DOI 10.1090/memo/0402
Hans-Otto Walther, The $2$-dimensional attractor of $x’(t)=-\mu x(t)+f(x(t-1))$, Mem. Amer. Math. Soc. 113 (1995), no. 544, vi+76. MR 1230775, DOI 10.1090/memo/0544
- [D]
- P. Dormayer, An attractivity region for characteristic multipliers of special symmetric solutions of
, J. Math. Anal. Appl. 168 (1992), 70-91. MR 1180674 (93m:34105)
- [H]
- G. E. Hutchinson, Circular causal systems in ecology, Ann. New York Acad. Sci., vol. 50, New York Acad. Sci., New York, 1948, pp. 221-246.
- [KM]
- S. Kakutani and L. Markus, On the nonlinear difference-differential equation
![$ y'(t) = [A - By(t - \tau )]y(t)$](images/img2.gif)
, Contributions to the Theory of Nonlinear Oscillations IV, Princeton Univ. Press, Princeton, NJ, 1958. MR 0101953 (21:755)
- [L]
- B. Lani-Wayda, Hyperbolic sets, shadowing and persistence for noninvertible mappings in Banach spaces, preprint, Univ. München, 1992. MR 1471208 (98i:58181)
- [MS]
- J. Mallet-Paret and G. Sell, Systems of delay differential equations with discrete Lyapunov functions, preprint, Brown Univ., Providence, RI, 1993.
- [N]
- R. D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of
, J. Differential Equations 34 (1979), 25-54. MR 549582 (81f:34073)
- [S]
- R. A. Smith, Poincaré-Bendixson theory for certain retarded functional differential equations, Differential Integral Equations 5 (1992), 213-240. MR 1141738 (93f:34128)
- [SW]
- H. Steinlein and H. O. Walther, Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for
-maps in Banach spaces, J. Dynamics Differential Equations 2 (1992), 325-365. MR 1066620 (92b:58170)
- [Wl]
- H. O. Walther, Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations, Mem. Amer. Math. Soc., vol. 79, no. 402, Amer. Math. Soc., Providence, RI, 1989. MR 979430 (90m:58184)
- [W2]
- -, The 2-dimensional attractor of
, Mem. Amer. Math. Soc., vol. 113, no. 544, Amer. Math. Soc., Providence, RI, 1995 (to appear). MR 1230775 (95f:58070)
Review Information:
Reviewer:
Hans-Otto Walther
Journal:
Bull. Amer. Math. Soc.
32 (1995), 132-136
DOI:
https://doi.org/10.1090/S0273-0979-1995-00551-3
