Publications de Ricardo Uribe-Vargas


1.- A Projective Invariant for Swallowtails and Godrons,
and Global Theorems on the Flecnodal Curve.

Moscow Mathematical Journal 6:4 (2006) 731-768.

2.- Arithmetics of the numbers of orbits of the Fermat-Euler dynamical systems.
Functional Analisis and Other Mathematics 1:1 (2006) 71-83.

3.- On Vertices, Focal Curvatures and Differential Geometry of Space Curves.
Bull. of the Brazilian Math. Soc., 36:3 (2005) 285-307.

4.- Topology of Dynamical Systems in
Finite Groups and Number Theory.

Bull. Sci. Math. 130:5 (2006) 377-402.

5.- On Singularities, "Perestroikas" and Differential Geometry of Space Curves.
L'Enseignement Mathématique, t.50 (2004) 69-101.

6.- 4-Vertex Theorems, Sturm Theory and Lagrangian Singularities.
Mathematical Physics, Analysis and Geometry, 7:3 (2004) 223-237.

7.- On Polar Duality, Lagrange and Legendre Singularities and Stereographic Projection to Quadrics.
Proc. of London Math. Soc., 87:3, November, 2003, 701-724.

8.- Rigid Body Motions and Arnold's Theory of Fronts on S2.
Journal of Geometry and Physics, 45:1-2 (2003) 91-104.

9.- On the Stability of Bifurcation Diagrams Associated to Vanishing Singularities.
Funct. Anal. and its Appl., 37:3 (2003) 236-240.

10.- On the Theory of Fronts on the 2-Sphere and the Theory of Space Curves.
(Proc. of Suzdal Int. Conf. 2002 on Diff. Eqs. and Dyn. Syst.)
J. of Math. Sciences 126:4 (2005) 1344-1353.

11.- On 4-Flattening Theorems and the Curves of Carathéodory, Barner and Segre.
Journal of Geometry, 77 (2003) 184-192.

12.- Weak Convexity does not Imply Convexity for Curves in RPn, n>2.
C.R. Acad. Sci. Paris, t.335, Série I, p. 47-52, 2002.

13.- Four-Vertex Theorems in Higher Dimensional Spaces for a Larger Class of Curves than the Convex Ones.
C.R. Acad. Sci. Paris, t.330, Série I, p. 1085-1090, 2000.

14.- On the (2k+2)-vertex and (2k+2)-flattening theorems in higher dimensional Lobatchevskian space.
C.R. Acad. Sci. Paris, t.325, Série I, p. 505-510, 1997.

15.- On the higher dimensional four-vertex theorem.
C.R. Acad. Sci. Paris, t.321, Série I, p. 1353-1358, 1995.

Prépublications-articles soumis

1.- Surface Evolution, Implicit Differential
Equations and Pairs of Legendrian Fibrations

Articles en préparation

1.- A graphic version of Shanks' algorithm in finite groups (by the monads).
2.- Revisiting the 4-vertex theorem for the ``newborn'' curves.
3.- On the lines of principal curvature at the godrons of smooth surfaces.
4.- A geometric invariant of the hyperbonodes of surfaces.
5.- Lectures on Legendrian and Lagrangian Singularities in
Elementary Differential Geometry.

6.- Arithmetics of the numbers of orbits of
the Fermat-Euler dynamical systems II.

7.- (avec Peter Giblin) On tangent sections of a surface and its vertex curve.
8.- (avec E. Munguia) On the Tropical Version of Desargues Theorem.

Autres publications

1.- Participation dans le livre Arnold Problems, Springer Verlag, 2004.
Commentaire
2.- Livre : Geometry, "in print" dans Cambridge Univ. Press
(avec V.I. Arnold et G. Capitanio). Commentaire sur le livre

Thèse d'Habilitation :

Contribution à la géométrie des sous-variétés
via les singularités en géométrie de contact (et symplectique)


Rapport sur ma thèse d'habilitation par S. Tabachnikov (Pennsylvania State Univesity)

Rapport sur ma thèse d'habilitation par V. Goryunov (University of Liverpool)