Displaying similar documents to “On complexity and motion planning for co-rank one sub-Riemannian metrics”

Sub-Riemannian sphere in Martinet flat case

A. Agrachev, B. Bonnard, M. Chyba, I. Kupka (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This article deals with the local sub-Riemannian geometry on ℜ, () where is the distribution ker being the Martinet one-form : and is a Riemannian metric on . We prove that we can take as a sum of squares . Then we analyze the flat case where 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence of our computations is to...

Density of paths of iterated Lévy transforms of brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.

Density of paths of iterated Lévy transforms of Brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform...

Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is  = d  + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...