Memoirs of the American Mathematical Society 1995; 76 pp; softcover Volume: 113 ISBN10: 0821826026 ISBN13: 9780821826027 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/113/544
 The equation \(x'(t) =  \mu x(t) + f(x(t1))\), with \(\mu \geq 0\) and \(xf(x) \le 0\) for \(0\neq x\in {\mathbb R}\), is a prototype for delayed negative feedback combined with friction. Its semiflow on \(C=C([1,0],{\mathbb R})\) leaves a set \(S\) invariant, which also plays a major role for the dynamics on the full space \(C\). The main result determines the attractor of the semiflow restricted to the closure of \(S\) for monotone, bounded, smooth \(f\). In the course of the proof, Walther derives PoincaréBendixson theorems for differentialdelay equations. The method used here is unique in its use of winding numbers and homotopies in nonconvex sets. Readership Researchers and graduate students studying dynamical systems and differential delay equations. Table of Contents  Introduction
 Notation, preliminaries
 Basic properties of solutions
 Attractors
 Phase space decomposition
 Apriori estimates, phase curves with trivial \(\alpha\)limit set, and invariant manifolds
 Graph representation
 Transversals
 Angles along projected phase curves
 The PoincaréBendixson theorem
 Proof of Theorem 7.1(ii)
 References
