Geodesic
On Pontryagin's First Direct Method in Pursuit Problems
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 163-167

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We describe an example of a three-dimensional linear differential game with convex compact sets of control. In this example, the integrand in Pontryagin's first direct method is discontinuous on a set of positive measure.
Keywords: linear differential game, Pontryagin direct method, convex compact set of control, stroboscopic strategy, Lebesgue measurability, Borel measurability, Aumann integral, Hausdorff metric, Cantor discontinuum. 
@article{MZM_2011_90_2_a0,
     author = {A. A. Azamov},
     title = {On {Pontryagin's} {First} {Direct} {Method} in {Pursuit} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--167},
     publisher = {mathdoc},
     volume = {90},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a0/}
}
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A. A. Azamov. On Pontryagin's First Direct Method in Pursuit Problems. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 163-167. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a0/