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Introduction

The delay differential equation and the hypotheses

The separatrix

The leading unstable set of the origin Oscillation frequencies Graph representations

Dynamics on $\overline W$ and disk representation of $\overline W \cap S$

Minimal linear instability of the periodic orbit $\mathcal O$

Smoothness of $W \cap S$ in case $\mathcal O$ is hyperbolic Smoothness of $W \cap S$ in case $\mathcal O$ is not hyperbolic

The unstable set of $\mathcal O$ contains the nonstationary points of bd$W$ bd$W$ contains the unstable set of the periodic orbit $\mathcal O$ $H \cap \overline W$ is smooth near $p_0$ Smoothness of $\overline W$, bd$W$ and $\overline W \cap S$

Homeomorphisms from bd$W$ onto the sphere and the cylinder

Homeomorphisms from $\overline W$ onto the closed ball and the solid cylinder

Resume Equivalent norms, invariant manifolds, Poincare maps and asymptotic phases

Smooth center-stable manifolds for $C^1$-maps Smooth generalized center-unstable manifolds for $C^1$-maps

Invariant cones close to neutrally stable fixed points with 1-dimensional center spaces

Unstable sets of periodic orbits

A discrete Lyapunov functional and a-priori estimates

Floquet multipliers for a class of linear periodic delay differential equations

Some results from topology

Bibliography

Index

Introduction

The delay differential equation and the hypotheses

The separatrix

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