Publications:

Mean Curvature flow:

Ao Sun, J. Xue, Generic mean curvature flows with cylindrical singularities, Arxiv: 2210.00419, 

Ao Sun, J. Xue, Generic regularity of Level Set Flows with spherical singularity,  Arxiv: 2204.07896

Ao Sun, J. Xue,  Initial Perturbation of the Mean Curvature Flow for conical limit shrinker, Arxiv: 2107.05066

Ao Sun, J. Xue,  Initial Perturbation of the Mean Curvature Flow for closed limit shrinker, Arxiv: 2104.03101

General Relativity:

J. Xue,  Arnold diffusion and geodesic dynamics of blackholes, arXiv: 2020.03047. 

J. Xue,  KAM and geodesic dynamics of blackholes, arXiv: 2020.03046,. 

group actions:

S. Hurtado, J. Xue,  A Tits alternative for surface group diffeomorphisms and  Abelian-by-Cyclic actions on surfaces containing an Anosov diffeomorphism, arXiv:1909.10112, to appear in Geometry & Topology. 

A. Wilkinson, J. Xue,  Rigidity of some abelian-by-cyclic solvable group actions on T^N, Communications in Mathematical Physics, 376, 1223–1259 (2020).

Hyperbolic dynamics: 

A. Blumenthal, J. Xue, L.-S. Young,  Lyapunov exponents for random perturbations of some area-preserving maps including the standard map.  Annals of Mathematics, Volume 185, no. 1, pages 285-310, 2017.

A. Blumenthal, J. Xue, L.-S. Young,  Lyapunov exponents and correlation decay for random perturbations of some prototypical 2D maps,  Communications in Mathematical Physics, 359.1 (2018): 347-373.

A. Blumenthal, J. Xue, Y. Yang, Lyapunov exponents for random perturbations of coupled standard maps, Arxiv: 2004.10626. to appear in Communications in Mathematical Physics. 

Arnold diffusion:

J. Xue,  Noncollision singularities in a planar four-body problem,  (solution of the Painlev\'e conjecture),  Acta Mathematica 224 (2020), 253--388. 

C.-Q. Cheng, J. Xue,  Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom, Sci China Math, 2023, 66.  (solution to the Arnold diffusion conjecture).

C.-Q. Cheng, J. Xue,  Variational approach to Arnold diffusion,  Science China Mathematics 62 (11), 2103-2130, special volume in honor of Professor Lo Yang's 80th birthday.

C.-Q. Cheng, J. Xue,  Recent developments on Arnold diffusion, to appear in MSRI proceedings. 

Hamiltonian dynamics, N-body problem

G. Huang, J. Xue, Super-hyperbolic orbits and non-collision singularities in a four-body problem,  Arxiv: 2302.12410

J. Gerver, G. Huang, J. Xue, A New Mechanism for Noncollision Singularities, Arxiv:  2202.08534

M.-C. Arnaud, J. Xue,  A C^1 Arnold-Liouville theorem, Asterisque, no 416, 2020, pp 1-33, special volume in memory of Yoccoz.

C.-Q. Cheng, J. Xue,  Order property and modulus of continuity of weak KAM solutions,  Calculus of variation and PDEs, 57.2 (2018): 65.

J. Xue, D. Dolgopyat,  Noncollision singularities in a planar two-center-two-body problem,  Communications in Mathematical Physics, August 2016, Volume 345, Issue 3, pp 797-879.

J. Xue,   Continuous averaging proof of the Nekhoroshev theorem,  DCDS-A, Vol 35, No.8, 2015.

J. Xue,   Arnold diffusion in a restricted planar four-body problem, Nonlinearity, 27 (2014) 2887-2908. 

J. Xue,  Nekhoroshev estimates for commuting nearly integrable symplectomorphisms,  Regular and Chaotic Dynamics, 22 (2017), no. 3, 248-265.

symplectic topology

Wenmin Gong, Zhijing Wang, J. Xue, Dynamics of composite symplectic Dehn twists, Arxiv: 2208.13041

J. Xue,  Closing lemma and KAM normal form, Arxiv: 2207.06208. 

W. Gong,  J. Xue,  Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits, arXiv:1902.00912. Nonlinearity, Vol 33, No. 12, Oct 2020. 

J. Xue,  Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on T^* T^n with application to non convex Hamiltonian systems,  Journal of Symplectic Geometry, Volume 15, no. 3, pages 905-936, 2017.