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Andrei Agrachev, Davide Barilari, and Ugo Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge Studies in Advanced Mathematics, 181, Cambridge University Press, Cambridge, (2020), From the Hamiltonian viewpoint, With an appendix by Igor Zelenko. MR 3971262
A. A. Agrachëv, Any sub-Riemannian metric has points of smoothness, Dokl. Akad. Nauk 424 (2009), no. 3, 295–298. MR 2513150
D. Barilari, Y. Chitour, F. Jean, D. Prandi, and M. Sigalotti, On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures, J. Math. Pures Appl. (9) 133 (2020), 118–138. MR 4044676
André Belotto da Silva, Alessio Figalli, Adam Parusiński, and Ludovic Rifford, Strong Sard conjecture and regularity of singular minimizing geodesics for analytic sub-riemannian structures in dimension 3, arXiv e-prints (2018), arXiv:1810.03347.
Francesco Boarotto, Roberto Monti, and Francesco Palmurella, Third order open mapping theorems and applications to the end-point map, arXiv e-prints (2019), arXiv:1907.11016.
N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, (1968). MR 0240238
Nicolas Bourbaki, Lie groups and Lie algebras. Chapters 1--3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, (1989), Translated from the French, Reprint of the 1975 edition. MR 979493
Francesco Boarotto and Davide Vittone, A dynamical approach to the Sard problem in Carnot groups, J. Differential Equations 269 (2020), no. 6, 4998–5033. MR 4104464
Y. Chitour, F. Jean, and E. Trélat, Genericity results for singular curves, J. Differential Geom. 73 (2006), no. 1, 45–73. MR 2217519
Chr. Golé and R. Karidi, A note on Carnot geodesics in nilpotent Lie groups, J. Dynam. Control Systems 1 (1995), no. 4, 535549. MR 1364562
Eero Hakavuori, ehaka/ode-abnormals: v1.0, Zenodo, jun 2020,
Marshall Hall, Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950), 575–581. MR 38336
Eero Hakavuori and Enrico Le Donne, Non-minimality of corners in subriemannian geometry, Invent. Math. 206 (2016), no. 3, 693704. MR 3573971
Lucas Hsu, Calculus of variations via the Griffiths formalism, J. Differential Geom. 36 (1992), no. 3, 551–589. MR 1189496
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti, and Davide Vittone, Extremal curves in nilpotent Lie groups, Geom. Funct. Anal. 23 (2013), no. 4, 1371–1401. MR 3077915
Enrico Le Donne, Gian Paolo Leonardi, Roberto Monti, and Davide Vittone, Extremal polynomials in stratified groups, Comm. Anal. Geom. 26 (2018), no. 4, 723–757. MR 3853926
Enrico Le Donne, Richard Montgomery, Alessandro Ottazzi, Pierre Pansu, and Davide Vittone, Sard property for the endpoint map on some Carnot groups, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 6, 1639–1666. MR 3569245
Enrico Le Donne and Roger Züst, Space of signatures as inverse limits of Carnot groups, arXiv e-prints (2019), arXiv:1910.04589.
Wensheng Liu and Héctor J. Sussman, Shortest paths for sub-Riemannian metrics on rank-two distributions, Mem. Amer. Math. Soc. 118 (1995), no. 564, x+104. MR 1303093
Richard Montgomery, Abnormal minimizers, SIAM J. Control Optim. 32 (1994), no. 6, 1605–1620. MR 1297101
Richard Montgomery, A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, 91, American Mathematical Society, Providence, RI, (2002). MR 1867362
Christophe Reutenauer, Free Lie algebras, London Mathematical Society Monographs. New Series, 7, The Clarendon Press, Oxford University Press, New York, (1993), Oxford Science Publications. MR 1231799
Sage Developers, SageMath, the Sage Mathematics Software System (Version 9.0), (2020),
H. J. Sussmann, A regularity theorem for minimizers of real-analytic subriemannian metrics, 53rd IEEE Conference on Decision and Control, Dec 2014, pp. 4801--4806.