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|d OCLCO
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|a (OCoLC)891385402
|z (OCoLC)1259244682
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|a QA3
|b .L58 1995eb
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| 082 |
0 |
4 |
|a 516.3/73
|2 20
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| 049 |
|
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|a UAMI
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| 100 |
1 |
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|a Liu, Wensheng,
|d 1962-
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PCjGgBGyP8hQ8ddYP4DrfxC
|
| 245 |
1 |
0 |
|a Shortest paths for sub-Riemannian metrics on rank-two distributions /
|c Wensheng Liu, Héctor J. Sussman.
|
| 264 |
|
1 |
|a Providence, Rhode Island, United States :
|b American Mathematical Society,
|c 1995.
|
| 264 |
|
4 |
|c ©1995
|
| 300 |
|
|
|a 1 online resource (121 pages)
|
| 336 |
|
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|a text
|b txt
|2 rdacontent
|
| 337 |
|
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|a computer
|b c
|2 rdamedia
|
| 338 |
|
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|a online resource
|b cr
|2 rdacarrier
|
| 490 |
1 |
|
|a Memoirs of the American Mathematical Society,
|x 0065-9266 ;
|v Volume 118, Number 564
|
| 500 |
|
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|a "November 1995, Volume 118, Number 564 (second of 5 numbers)"--Cover
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| 504 |
|
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|a Includes bibliographical references.
|
| 588 |
0 |
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|a Print version record.
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| 505 |
0 |
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|a 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
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| 505 |
8 |
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|a 5.1 The sub-Riemannian distance, length minimization and time optimality5.2 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
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| 505 |
8 |
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|a 9.2 3-Regular distributions9.3 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
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| 546 |
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|a English.
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| 590 |
|
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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| 650 |
|
0 |
|a Geometry, Riemannian.
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| 650 |
|
0 |
|a Geodesics (Mathematics)
|
| 650 |
|
6 |
|a Géométrie de Riemann.
|
| 650 |
|
6 |
|a Géodésiques (Mathématiques)
|
| 650 |
|
7 |
|a Geodesics (Mathematics)
|2 fast
|
| 650 |
|
7 |
|a Geometry, Riemannian
|2 fast
|
| 700 |
1 |
|
|a Sussmann, Hector J.,
|d 1946-
|e author.
|1 https://id.oclc.org/worldcat/entity/E39PCjKMMfFXWth74CGDMHCjT3
|
| 758 |
|
|
|i has work:
|a Shortest paths for sub-Riemannian metrics on rank-two distributions (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCFCh83YWBTkQGcj934H7QC
|4 https://id.oclc.org/worldcat/ontology/hasWork
|
| 776 |
0 |
8 |
|i Print version:
|a Liu, Wensheng, 1962-
|t Shortest paths for sub-Riemannian metrics on rank-two distributions.
|d Providence, Rhode Island, United States : American Mathematical Society, ©1995
|h ix, 104 pages
|k Memoirs of the American Mathematical Society ; Volume 118, Number 564
|z 9780821804049
|
| 830 |
|
0 |
|a Memoirs of the American Mathematical Society ;
|v Volume 118, no. 564.
|
| 856 |
4 |
0 |
|u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114000
|z Texto completo
|
| 936 |
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