We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

}, doi = {10.1007/s10883-011-9113-4}, url = {http://hdl.handle.net/1963/4914}, author = {Bernard Bonnard and Gr{\'e}goire Charlot and Roberta Ghezzi and Gabriel Janin} } @article {2006, title = {Stability of planar nonlinear switched systems}, number = {SISSA;04/2005/M}, year = {2006}, abstract = {We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 - u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,$\infty$) {\textrightarrow} {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields.}, url = {http://hdl.handle.net/1963/1710}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Mario Sigalotti} }