MATHEMATICAL PRELIMINARIES |

Banach spaces and examples |

Linear transformations |

Fixed point theorems |

GENERAL PROPERTIES OF DIFFERENTIAL EQUATIONS |

Existence |

Continuation of solutions |

Uniqueness and continuity properties |

Continuous dependence and stability |

Extension of the concept of a differential equation |

Differential inequalities |

Autonomous systems-generalities |

Autonomous systems-limit sets, invariant sets |

Remarks and suggestions for further study |

TWO DIMENSIONAL SYSTEMS |

Planar two dimensional systems-the Poincaré-Bendixson theory |

Differential systems on a torus |

Remarks and suggestions for further study |

LINEAR SYSTEMS AND LINEARIZATION |

General linear systems |

Stability of linear and perturbed linear systems |

nth Order scalar equations |

Linear systems with constant coefficients |

Two dimensional linear autonomous systems |

The saddle point property |

Linear periodic systems |

Hill’s equation |

Reciprocal systems |

Canonical systems |

Remarks and suggestion for further study |

PERTURBATION OF NONCRITICAL LINEAR SYSTEMS |

Nonhomogeneous linear systems |

Weakly nonlinear equations-noncritical case |

The general saddle point property |

More general systems |

The Duffing equation with large damping and large forcing |

Remarks and extensions |

SIMPLE OSCILLATORY PHENOMENA AND THE METHOD OF AVERAGING |

Conservative systems |

Nonconservative second order equations-limit cycles |

Averaging |

The forced van der Pol equation |

Duffing’s equation with small damping and small harmonic forcing |

The subharmonic of order 3 for Duffing’s equation |

Damped excited pendulum with oscillating support |

Exercises |

Remarks and suggestions for further study |

BEHAVIOR NEAR A PERIODIC ORBIT |

Stability of a periodic orbit |

Sufficient conditions for orbital stability in two dimensions |

Autonomous perturbations |

Remarks and suggestions for further study |

INTEGRAL MANIFOLDS OF EQUATIONS WITH A SMALL PARAMETER |

Methods of determining integral manifolds |

Statement of results |

A “nonhomgeneous linear” system |

The mapping principle |

Proof of Theorem 2.1 |

Stability of the perturbed manifold |

Applications |

Exercises |

Remarks and suggestions for further study |

PERIODIC SYSTEMS WITH A SMALL PARAMETER |

A special system of equations |

Almost linear systems |

Periodic solutions of perturbed autonomous equa |

Remarks and suggestions for further study |

ALTERNATIVE PROBLEMS FOR THE SOLUTION OF FUNCTIONAL EQUATIONS |

Equivalent equations |

A generalization |

Alternative problems |

Alternative problems for periodic solutions |

The Perron-Lettenmeyer theorem |

Remarks and suggestions for further study |

THE DIRECT METHOD OF LIAPUNOV |

Sufficient conditions for stability and instability in autonomous systems |

Circuits containing Esaki diodes |

Sufficient conditions for stability in nonautonomous systems |

The converse theorems for asymptotic stability |

Implications of asymptotic stability |

Wazewski’s principle |

Remarks and suggestions for further study |

APPENDIX |

ALMOST PERIODIC FUNCTIONS |

REFERENCES |

INDEX |