Local controllability bifurcations in families of bidynamical systems on the plane

V. I. Arnol’d, Ordinary Differential Equations (Nauka, Moscow, 1971; Springer, Berlin, 1992). V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps, 2nd ed. (MTsNMO, Moscow, 2004) [in Russian]. M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities (Springer, New York, 1973; Mir, Moscow, 1977). A. A. Davydov, “Singularities of Fields of Limiting Directions of Two-Dimensional Control Systems,” Mat. Sb. 136(4), 478–499 (1988) [Math. USSR, Sb. 64 (2), 471–493 (1989)]. M. A. Komarov, “Local Controllability in Generic Two-Parameter Families of Bidynamical Systems in the Plane,” Tr. Vladimir. Gos. Univ., No. 3, 66–75 (2007). N. N. Petrov, “On the Controllability of Autonomous Systems,” Diff. Uravn. 4(4), 606–617 (1968). L. Azevedo, “Transitividade local de sistemas polidinamicos,” Master Thesis (Dept. Math. Appl., Faculty Sci., Univ. Porto, Porto, 2006). B. Jakubczyk and W. Respondek, “Bifurcations of 1-Parameter Families of Control-Affine Systems in the Plane,” SIAM J. Control Optim. 44(6), 2038–2062 (2006). M. Rupniewski, “Local Bifurcations of Control-Affine Systems in the Plane,” J. Dyn. Control Syst. 13(1), 135–159 (2007). H. J. Sussmann, “A General Theorem on Local Controllability,” SIAM J. Control Optim. 25(1), 158–194 (1987).