Shortest paths for sub-Riemannian metrics on rank-two distributions / / Wensheng Liu, Héctor J. Sussman

• Autore: Liu Wensheng <1962->
• Pubblicazione: Providence, Rhode Island, United States : , : American Mathematical Society, , 1995; ©1995
• Descrizione fisica: 1 online resource (121 p.)
• Disciplina: 510 s
• Soggetto topico: Geometry, Riemannian; Geodesics (Mathematics)
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): SussmannHector J. <1946->
• Note generali: "November 1995, Volume 118, Number 564 (second of 5 numbers)"--Cover.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Table of Contents""; ""1 Introduction""; ""2 Three examples""; ""2.1 Riemannian geodesies""; ""2.2 The Heisenberg algebra case""; ""2.3 An abnormal minimizer""; ""3 Notational conventions and definitions""; ""3.1 Manifolds, charts, bundles, curves and arcs""; ""3.2 Hamiltonian functions, Hamilton vector fields, and bicharacteristics""; ""3.3 Hamiltonian lifts and characteristics""; ""3.4 Distributions, admissible curves, orbits""; ""3.5 Nonholonomic distributions; regularity""; ""4 Abnormal extremals""; ""5 Sub-Riemannian manifolds, length minimizers and extremals"" ; ""5.1 The sub-Riemannian distance, length minimization and time optimality""""5.2 Extremals""; ""5.3 The relationship between minimality and extremality""; ""6 Regular abnormal extremals for rank-two distributions""; ""6.1 The regular abnormal foliation of a rank-two distribution""; ""6.2 Regular abnormal biextremals of a sub-Riemannian manifold""; ""7 Local optimality of regular abnormal extremals""; ""7.1 The main inequality""; ""7.2 The normal form theorem""; ""7.3 The optimality theorem""; ""8 Strict abnormality""; ""9 Some special cases""; ""9.1 2- and 3-generating distributions"" ; ""9.2 3-Regular distributions""""9.3 The 4- and 5-dimensional cases""; ""9.4 The three-dimensional case""; ""9.5 A Lie group example""; ""9.6 A nonsmooth abnormal extremal""; ""Appendix A: The Gaveau-Brockett problem""; ""Appendix B: Proof of Theorem 1""; ""B.l: Control systems""; ""B.2: The Maximum Principle""; ""Appendix C: Local optimality of normal extremals""; ""Appendix D: Rigid sub-Riemannian arcs and local optimality""; ""Appendix E: A nonoptimality proof""; ""References""
• Titolo autorizzato: Shortest paths for sub-Riemannian metrics on rank-two distributions
• ISBN: 1-4704-0143-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480534003321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 118, Number 564.