Research
Research Interest:
Ergodic Theory and Dynamical Systems
Papers and preprints:
1. On mixing diffeomorphisms of the disc, with Artur Avila, Bassam Fayad, Patrice Le Calvez, Disheng Xu, in Inventiones mathematicae 220, 673-714 (2020).
2. On the spectrums of ergodic Schrodinger operators with finitely valued potentials, in Bulletin de la Société Mathématique de France 145 (2017), no. 2, 295-304.
3. Ballistic transport and absolute continuity of one-frequency Schrödinger operators, with Zhiyan Zhao, in Communications in Mathematical Physics. May 2017, Volume 351, Issue 3, pp 877-921.
4. On stable transitivity of finitely generated group of volume preserving diffeomorphisms, in Ergodic Theory and Dynamical Systems. Volume 39, Issue 2, February 2019, pp. 554-576.
5. On the smooth dependence of SRB measures for partially hyperbolic systems, in Communications in Mathematical Physics. Februrary 2018, Volume 358, Issue 1, pp 45-79.
6. An effective version of Katok's horseshoe theorem for conservative $C^2$ surface diffeomorphisms, with B. Fayad, in Journal of Modern Dynamics, 11 (2017), 425-445.
7. $C^{r}-$prevalence of stable ergodicity for a class of partially hyperbolic systems, with Martin Leguil, in J. Eur. Math. Soc. 24, No. 9, 3379-3438 (2022).
8. On topological genericity of the mode-locking phenomenon, in Mathematische Annalen, 376, 707-728 (2020).
9. The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan, with Jian Wang, in Geometric and Functional Analysis. October 2018, Volume 28, Issue 5, pp 1487-1516.
10. Density of mode-locking property for quasi-periodically forced Arnold circle maps, with J. Wang, to appear in Ergodic Theory and Dynamical Systems.
11. $C^1$ actions on manifolds by lattices in Lie groups, with Aaron Brown and Danijela Damjanović, in Compositio Mathematica, 158 (2022), 529–549.
12. Zimmer's conjecture for lattice actions: the ${\rm SL}(n, \C)$-case, arXiv.
(to be replaced by item 17)
13. Smooth mixing Anosov flows in dimension three are exponentially mixing, with Masato Tsujii, in Annals of Mathematics, 197 (2023), Issue 1, 65-158.
14. On bifurcation of statistical properties of partially hyperbolic endomorphisms, with M. Tsujii, to appear in Ergodic Theory and Dynamical Systems.
15. On pseudo-rotations of the annulus with generic rotation number, with Barney Bramham, arXiv.
16. Geometric properties of partially hyperbolic measures and applications to measure rigidity, with Alex Eskin and Rafael Potrie, arXiv.
Work in progress:
17. Zimmer's conjecture for non-split semisimple Lie groups, with Jinpeng An and A. Brown.
18. Limit distributions for simultaneous Diophantine approximations, with Dmitry Dolgopyat and B. Fayad.
Survey article:
Recent results and open questions on pseudo-rotations, with B. Bramham, to appear in book <<A Vision for Dynamics in the 21st Century>>