Bulletin of the American Mathematical Society

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Book Information:

Authors: Ovidiu Calin and Der-Chen Chang
Title: Sub-Riemannian geometry: general theory and examples
Additional book information: Encyclopedia of Mathematics and Its Applications, vol.~126, Cambridge University Press, New York, 2009, xi+367 pp., ISBN 978-0521897303, US$99.00, hardcover

M. Born, Natural Philosophy of Cause and Chance, Oxford Press, 1949.

Luca Capogna, Donatella Danielli, Scott D. Pauls, and Jeremy T. Tyson, An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem, Progress in Mathematics, vol. 259, Birkhäuser Verlag, Basel, 2007. MR 2312336, DOI 10.1007/978-3-7643-8133-2

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A. Chenciner, Collisions totales, mouvements complètement paraboliques et réduction des homothéties dans le problème des $n$ corps, Regul. Chaotic Dyn. 3 (1998), no. 3, 93–106 (French, with French and Russian summaries). J. Moser at 70 (Russian). MR 1704972, DOI 10.1070/rd1998v003n03ABEH000083

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Mikhael Gromov, Carnot-Carathéodory spaces seen from within, Sub-Riemannian geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 79–323. MR 1421823

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Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081

Richard Montgomery, A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. MR 1867362, DOI 10.1090/surv/091

G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, No. 78, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973. MR 0385004

P. K. Rashevskii, About connecting two points of complete nonholonomic space by admissible curve, Uch. Zapiski Ped. Inst. Libknexta, no. 2, 83-94, (1938) [Russian].

A. Shapere and F. Wilczek, Self-propulsion at low Reynolds number, Physical Review Letters, vol. 58, 2051-2054, (1987).

Robert S. Strichartz, Realms of mathematics: elliptic, hyperbolic, parabolic, sub-elliptic, Math. Intelligencer 9 (1987), no. 3, 56–64. MR 895772, DOI 10.1007/BF03023957

Noboru Tanaka, On the equivalence problems associated with simple graded Lie algebras, Hokkaido Math. J. 8 (1979), no. 1, 23–84. MR 533089, DOI 10.14492/hokmj/1381758416

L.C. Young, Lectures on the Calculus of Variations and Optimal Control Theory, Chelsea, 1980.

• M. Born, Natural Philosophy of Cause and Chance, Oxford Press, 1949.
• L. Capogna, D. Danielli, Donatella, S. Pauls, and J. Tyson, An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem. Progress in Mathematics, 259. Birkhäuser Verlag, Basel, 2007. MR 2312336 (2009a:53053)
• E. Cartan, Les systèmes de Pfaff à cinque variables et lès équations aux dérivées partielles du second ordre, Ann. Sci. Ècole Normale, no. 3, 27, 109-192, (1910). MR 1509120
• A. Chenciner, De l’espace des triangles au probleme des $3$ corps, web page: http://www.imcce.fr/Equipes/ASD/person/chenciner/chen_preprint.php, under the year 2004. MR 1704972 (2000h:70023)
• W.L. Chow, Uber Systeme van Linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann., vol. 117, 98-105, (1939). MR 0001880 (1:313d)
• M. Gromov, Carnot-Caratheodory spaces seen from within, pp. 79-323 in Sub-Riemannian Geometry, A. Bellaiche and J-J. Risler, eds., Birhauser, Basel, Switzerland, (1996). MR 1421823 (2000f:53034)
• M. Gromov, Groups of Polynomial Growth and Expanding Maps, Publ. Math. IHES, 53, 53-73, (1981). MR 623534 (83b:53041)
• L. Hörmander, Hypoelliptic second order differential operators, Acta. Math., 119, 147-171, (1967). MR 0222474 (36:5526)
• R. Montgomery, A tour of sub-Riemannian geometries, their geodesics and applications, Math. Surveys Monogr., vol. 91, American Mathematical Society, Providence, RI, 2002. MR 1867362 (2002m:53045)
• G.D. Mostow, Strong Rigidity of Locally Symmetric Spaces, Ann. of Math. Stud., vol. 78, Princeton Univ. Press, (1973). MR 0385004 (52:5874)
• P. K. Rashevskii, About connecting two points of complete nonholonomic space by admissible curve, Uch. Zapiski Ped. Inst. Libknexta, no. 2, 83-94, (1938) [Russian].
• A. Shapere and F. Wilczek, Self-propulsion at low Reynolds number, Physical Review Letters, vol. 58, 2051-2054, (1987).
• R. Strichartz, Realms of mathematics: elliptic, hyperbolic, parabolic, sub-elliptic, Math. Intelligencer, 9, no. 3, 56–64 (1987). MR 895772 (88h:35002)
• N. Tanaka, On the equivalence problem associated with simple graded Lie algebras, Hokkaido Math. Journal, v. 8, 23-84, 1979. MR 533089 (80h:53034)
• L.C. Young, Lectures on the Calculus of Variations and Optimal Control Theory, Chelsea, 1980.