Sturm theory, ghys theorem on zeroes of the Schwarzian derivative and flattening of legendrian curves

Selecta Mathematica, New Series

Volumn 2, Issue 2, 1996, Pages 297-307

  Ovsienko, V ^a   Tabachnikov, S ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSITY OF ARKANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002507992     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/BF01587937     Document Type: Article

References (15)

1. P. Appel. Sur les propriétés des cubiques gauches et le mouvement hélicoidal d'un corps solide. Thèse, Paris 1876.
2. 4, hyperbolicity and projective topology. Sib. Math. Journal 29 (1988), n.5, 36-47.
3. V. I. Arnold. Topological invariants of plane curves and caustics. AMS Univ. Lecture Series N.5, Providence, 1994.
4. V. I. Arnold. On the number of flattening points on space curves. Preprint Inst. Mittag-Leffler, 1994.
5. V. I. Arnold. Remarks on the sextactic and other points of plane curves. Preprint, 1995.
6. V. I. Arnold. On topological properties of Legendre projections in contact geometry of wave fronts. Algebra i Analysis (S. Petersbourg Math. J.) 6 (1994).
7. V. I. Arnold. Geometry of spherical curves and algebra of quaternions. Uspekhi Mat. Nauk 50 (1995), n.1, 3-68. (Russian)
8. E. Ghys. Cercles osculateurs et géométrie lorentzienne. Talk at the journée inaugurale du CMI, Marseille, February 1995.
9. L. Guieu, E. Mourre, V. Yu. Ovsienko. Theorem on six vertices of a plane curve via the Sturm theory. Preprint CPT, 1995.
10. A. Hurwitz. Über die Fourierschen Konstanten integrierbarer Funktionen. Math. Ann. 57 (1903), 425-446.
11. S. Mukhopadhyaya. New Methods in the Geometry of a Plane Arc. Bull. Calcutta Math. Soc. 1 (1909), 32-47.
12. J. C. F. Sturm. Mémoire sur les équations différentielles du second ordre. J. Math. Pures Appl. 1 (1836), 106-186.
13. S. Tabachnikov. Around four vertices. Russian Math. Surveys 45 (1990), n.1, 229-230.
14. S. Tabachnikov. The four vertex theorem revisited - Two variations on the old theme. Preprint I. Newton Inst., 1995.
15. S. Tabachnikov. On Zeroes of the Schwarzian Derivative. MPIM Preprint, 1996.