Characterization of feedback linearizable systems for continuous time (Jakubczyk and Respondek 1980), and discrete time systems (Jakubczyk 1986)
Introducing a geometric language for analysis of nonlinear discrite-time systems (Jakubczyk and Sontag, SIAM J. Control and Optimiz. 1990). This language was later used in similar contexts by other authors
Finding criteria for existence of nonlinear realisations (Jakubczyk, SIAM J. Control and Optimiz. 1980 and 1986). The approach was later used by J.P. Gauthier et al. for systems on Lie groups. Another approach using noncommutative formal power series was proposed by M. Fliess (Invent. Math. 1983) and was later completed by Jakubczyk (Ann. Polon. Math. 2000)
Presenting effective criteria for quasi-homogeneity of singular varieties, concluding from them a version of relative Poincare lemma needed for solving a Moser homotopy equation for closed differential 2-forms (W. Domitrz, S. Janeczko and M. Zhitomirskii 2004)
Finding basic symplectic invariants and symplectic classification of singular curves (Domitrz, Janeczko and Zhitomirskii, J. Reine Angew. Math. 2008). These results considerably extend earlier ideas and results of V.I. Arnold
Discovering natural conformal geometries hidden in ODEs considered modulo contact or point transformations (Nurowski, J. Geometry and Physics 2005). Identifying a nonstandard irreducible SO (3) geometry in dimension five (Bobienski and Nurowski, J. Reine Angew. Math. 2007)
A general solution to an optimal motion planning problem for 1-step generating distributions (Gauthier, Jakubczyk and Zakalyukin, SIAM J. Control and Optimiz. 2010). Identification of canonical, fast oscillating controls in the case of free nilpotent approximation
Identifying invariants of distributions of corank 2 (Jakubczyk, Krynski and Pelletier, Ann. Inst. H. Poincare 2009, Krynski and Zelenko 2010).
