Marie-Claude Arnaud - Selected Publications#

1. A C1 Arnold-Liouville theorem, with Jinxin Xue.
To appear in Astérisque, Yoccoz memorial volume.

2. A multidimensional Birkhoff theorem for time-dependent Tonelli Hamiltonians, with Andrea Venturelli. Calc. Var. Partial Differential Equations, 56 (2017), no. 4, 27 p.

3. Lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions.
Comm. Math. Phys., 343 (2016), no. 3, p. 783–810.

4. with P. Berger. The non-hyperbolicity of irrational invariant curves for twist maps and all that follows, preprint sur HAL, Revista Matemática Iberoamericana number 32.4 (2016) pp. 1295–1310

5. Boundaries of instability zones for symplectic twist maps.
J. Inst. Math. Jussieu, 13 (2014), no. 1, 1941.

6. Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet’s splitting, Ergodic Theory and Dynamical Systems, volume 33, issue 03, (2013), pp. 693-712 .

7. Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures.
Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), no. 6, p. 989–1007.

8. The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents.
Ann. of Math. (2), 174 (2011), no. 3, p. 1571–1601.

9. On a theorem due to Birkhoff. Geom. Funct. Anal., 20 (2010), no. 6, p. 1307–1316.

10. Three results on the regularity of the curves that are invariant by an exact symplectic twist map.
Publ. Math. Inst. Hautes Etudes Sci., 109 (2009), p. 1–17.

11. Fibrés de Green et régularité des graphes C0-lagrangiens invariants par un flot de Tonelli,Annales Henri Poincaré 9 (5) (2008), 881-926

12. Création de connexions en topologie C1.
Ergodic Theory Dynam. Systems, 21 (2001), p. 339–381.

13. Le "Closing Lemma" en topologie C1, Supplément au Bull. Soc. Math. Fr. 74 (1998)