Finite-dimensional reductions of smooth extremal problems

Abstract

Contents Introduction Chapter I. Dimension lowering in finite-dimensional extremal problems §1.1. The Poincaré reduction §1.2. The generalized Poincaré reduction §1.3. Postcritical equilibrium states of an elastic chain §1.4. Stationary rotations of multidimensional tops. The Smale reduction Chapter II. Finite-dimensional reductions in smooth extremal problems on infinite-dimensional manifolds §2.1. The Lyapunov-Schmidt reduction §2.2. The Morse-Bott reduction §2.3. General finite-dimensional reduction scheme §2.4. Elastic equilibria of the Euler rod §2.5. Morse-Bott reduction for the Kirchhoff rod §2.6. Equilibria of a thin elastic plate Bibliography