Search results for "Almost-Riemannian geometry"

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Optimal control and Clairaut-Liouville metrics with applications

2014

The work of this thesis is about the study of the conjugate and cut loci of 2D riemannian or almost-riemannian metrics. We take the point of view of optimal control to apply the Pontryagin Maximum Principle in the purpose of characterize the extremals of the problem considered.We use geometric, numerical and integrability methods to study some Liouville and Clairaut-Liouville metrics on the sphere. In the degenerate case of revolution, the study of the ellipsoid uses geometric methods to fix the cut locus and the nature of the conjugate locus in the oblate and prolate cases. In the general case, extremals will have two distinct type of comportment which correspond to those observed in the r…

Ising chains of spinsLiouville metricsCut LocusContrôle optimal géométrique[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Almost-Riemannian geometryChaînes de spins de type IsingGeometric optimal control[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]Conjugate Locus[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Métriques de LiouvilleMétrique pseudo-riemannienneLieu conjugué[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Lieu de coupure
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