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V. I. Arnold, Ordinary differential equations. "; $programm ="

Processes described by ODE.

Examples from ecology, mechanics, electricity.

Elementary methods of integration and symmetries.

General theory: existence and uniqueness of solutions in real and complex domains.

Small parameter method.

Linear theory.

Phase flows of linear vector fields and exponentials of linear operators.

Linear equations of higher order.

Resonance.

Small amplitude oscillations.

Stability of singular and fixed points.

Limit cycles and their stability.

Poincare-Bendixson theorem.

The Smale horseshoe.

Linear equations in the complex domain.

Monodromy group.

Elements of Frobenius theory."; ?>