1 Linear differential difference equations. - 1. 1 Differential and difference equations. - 1. 2 Retarded differential difference equations. - 1. 3 Exponential estimates of x(? f). - 1. 4 The characteristic equation. - 1. 5 The fundamental solution. - 1. 6 The variation-of-constants formula. - 1. 7 Neutral differential difference equations. - 1. 8 Supplementary remarks. - 2 Retarded functional differential equations : basic theory. - 2. 1 Definition. - 2. 2 Existence uniqueness and continuous dependence. - 2. 3 Continuation of solutions. - 2. 4 Differentiability of solutions. - 2. 5 Backward continuation. - 2. 6 Caratheodory conditions. - 2. 7 Supplementary remarks. - 3 Properties of the solution map. - 3. 1 Finite- or infinite-dimensional problem?. - 3. 2 Equivalence classes of solutions. - 3. 3 Exponential decrease for linear systems. - 3. 4 Unique backward extensions. - 3. 5 Range in ?n. - 3. 6 Compactness and representation. - 3. 7 Supplementary remarks. - 4 Autonomous and periodic processes. - 4. 1 Processes. - 4. 2 Invariance. - 4. 3 Discrete systemsmaximal compact invariant sets. - 4. 4 Fixed points of discrete dissipative processes. - 4. 5 Stability and maximal invariant sets in processes. - 4. 6 Periodic trajectories of ?-periodic processes. - 4. 7 Convergent systems. - 4. 8 Supplementary remarks. - 5 Stability theory. - 5. 1 Definitions. - 5. 2 The method of Liapunov functional. - 5. 3 Liapunov functional for autonomous systems. - 5. 4 Razumikhin-type theorems. - 5. 5 Supplementary remarks. - 6 General linear systems. - 6. 1 Global existence and exponential estimates. - 6. 2 Variation-of-constants formula. - 6. 3 The formal adjoint equation. - 6. 4 The true adjoint. - 6. 5 Boundary-value problems. - 6. 6 Stability and boundedness. - 6. 7 Supplementary remarks. - 7 Linear autonomous equations. - 7. 1 The semigroup and infinitesimalgenerator. - 7. 2 Spectrum of the generator-decomposition of C. - 7. 3 Decomposing C with the formal adjoint equation. - 7. 4 Estimates on the complementary subspace. - 7. 5 An example. - 7. 6 The decomposition in the variation-of-constants formula. - 7. 7 Supplementary remarks. - 8 Linear periodic systems. - 8. 1 General theory. - 8. 2 Decomposition. - 8. 3 Supplementary remarks. - 9 Perturbed linear systems. - 9. 1 Forced linear systems. - 9. 2 Bounded almost-periodic and periodic solutions; stable and unstable manifolds. - 9. 3 Periodic solutionscritical cases. - 9. 4 Averaging. - 9. 5 Asymptotic behavior. - 9. 6 Boundary-value problems. - 9. 7 Supplementary remarks. - 10 Behavior near equilibrium and periodic orbits for autonomous equations. - 10. 1 The saddle-point property near equilibrium. - 10. 2 Nondegenerate periodic orbits. - 10. 3 Hyperbolic periodic orbits. - 10. 4 Supplementary remarks. - 11 Periodic solutions of autonomous equations. - 11. 1 Hopf bifurcation. - 11. 2 A periodicity theorem. - 11. 3 Range of the period. - 11. 4 The equation $$\dot x(t) = - \alpha x(t - 1)[1 + x(t)]$$. - 11. 5 The equation $$\dot x(t) = - \alpha x(t - 1)[1 - {x^2}(t)]$$. - 11. 6 The equation $$\ddot x(t) + f(x(t))\dot x(t) + g(x(t - r)) = 0$$. - 11. 7 Supplementary remarks. - 12 Equations of neutral type. - 12. 1 Definition of a neutral equation. - 12. 2 Fundamental properties. - 12. 3 Linear autonomous D operators. - 12. 4 Stable D operators. - 12. 5 Strongly stable D operators. - 12. 6 Properties of equations with stable D operators. - 12. 7 Stability theory. - 12. 8 General linear equations. - 12. 9 Stability of autonomous perturbed linear systems. - 12. 10 Linear autonomous and periodic equations. - 12. 11 Nonhomogeneous linear equations. - 12. 12 Supplementary remarks. - 13 Global theory. - 13. 1 Generic properties of retarded equations. - 13. 2 Theset of global solutions. - 13. 3 Equations on manifolds : definitions. - 13. 4 Retraded equations on compact manifolds. - 13. 5 Further properties of the attractor. - 13. 6 Supplementary remarks. - Appendix Stability of characteristic equations. Language: English