Vershik, A. M.; Gershkovich, V. Ya. Nonholonomic dynamical systems, geometry of distributions and variational problems. (English. Russian original) Zbl 0797.58007 Dynamical systems. VII. Encycl. Math. Sci. 16, 1-81 (1994); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 16, 5-85 (1987). [For the entire Russian collection see Zbl 0639.00034.]Contents: Chapter 1. Geometry of distributions. §1. Distributions and related objects. §2. Generic distributions and sets of vector fields, and degeneracies of small codimension. Nilpotentization and classification problem. Chapter 2. Basic theory of nonholonomic Riemannian manifolds. §1. General nonholonomic variational problem and the geodesic flow on nonholonomic Riemannian manifolds. §2. Estimates of the accessibility set.Chapter 3. Nonholonomic variational problems on three-dimensional Lie groups. §1. The nonholonomic \(\varepsilon\)-sphere and the wave front. §2. Nonholonomic geodesic flow on three-dimensional Lie groups. Cited in 2 ReviewsCited in 107 Documents MSC: 58-02 Research exposition (monographs, survey articles) pertaining to global analysis 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 58A30 Vector distributions (subbundles of the tangent bundles) 58D27 Moduli problems for differential geometric structures 58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable) Keywords:survey; geometry of distributions; variational dynamics Citations:Zbl 0639.00034 PDFBibTeX XMLCite \textit{A. M. Vershik} and \textit{V. Ya. Gershkovich}, Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya None, 5--85 (1987; Zbl 0797.58007); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 16, 5--85 (1987)