On the role of abnormal minimizers in sub-riemannian geometry
Copyright policy )On the role of abnormal minimizers in sub-riemannian geometry
Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^��)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.
sub-Riemannian manifolds, sphere and wave-front with small radii, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Sub-Riemannian geometry, optimal control, abnormal minimizers, sub-Riemannian geometry, Existence theories for optimal control problems involving ordinary differential equations, optimal control problem, Martinet geometry, Optimization and Control (math.OC), FOS: Mathematics, singular trajectories, Mathematics - Optimization and Control, geodesics
sub-Riemannian manifolds, sphere and wave-front with small radii, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Sub-Riemannian geometry, optimal control, abnormal minimizers, sub-Riemannian geometry, Existence theories for optimal control problems involving ordinary differential equations, optimal control problem, Martinet geometry, Optimization and Control (math.OC), FOS: Mathematics, singular trajectories, Mathematics - Optimization and Control, geodesics
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