47 citations · 95 across the 21 of their papers we have counts for
25 papers
Mean curvature flows with cylindrical singularities II: stability and genericity
Ao Sun, Jinxin Xue
In [SX25], we introduced the notion of nondegenerate cylindrical singularity using the ideas from dynamical systems. In this paper, we further study the properties of these singula…
On Aubry's completeness conjecture
Tianqi Shi, Jinxin Xue
In this paper, we prove Aubry's completeness stating conjecture that for a twist map the graph of rotation numbers as a function of the cohomology classes is a purely singularly co…
Super-hyperbolic orbits and non-collision singularities in a four-body problem
Guan Huang, Jinxin Xue
In this paper, we prove the existence of super-hyperbolic orbits in four-body problem, which solves a conjecture of Marchal-Saari. We also prove the existence of noncollision singu…
Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy
Ao Sun, Jinxin Xue
This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalize…
Dynamics of composite symplectic Dehn twists
Wenmin Gong, Zhijing Wendy Wang, Jinxin Xue
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form…
Closing lemma and KAM normal form
Jinxin Xue
In this paper, we develop an approach to the problem of closing lemma based on KAM normal form. The new approach differs from existing perturbation approach and spectral appr…
Generic regularity of Level Set Flows with spherical singularity
Ao Sun, Jinxin Xue
The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularit…
A New Mechanism for Noncollision Singularities
Joseph Gerver, Guan Huang, Jinxin Xue
In this paper, we prove the existence of noncollision singularities in a planar four-body problem in a model different from [J. Xue,Acta Math.V224(2)253-388, 2020.]. In this model,…
Generic Dynamics of Mean Curvature Flows with Asymptotically Conical Singularities
Ao Sun, Jinxin Xue
This is the second paper in the series to study the generic dynamics of mean curvature flows. We study the initial perturbation of mean curvature flows, whose first singularity is…
Initial Perturbation of the Mean Curvature Flow for closed limit shrinker
Ao Sun, Jinxin Xue
This is a contribution to the program of dynamical approach to mean curvature flow initiated by Colding and Minicozzi. In this paper, we prove two main theorems. The first one is l…
Arnold diffusion and geodesic dynamics of blackholes
Jinxin Xue
In this paper, we study the chaotic motion of a massive particle moving in a perturbed Schwarzschild or Kerr background. We discover three novel orbits that do not exist in the unp…
KAM and geodesic dynamics of blackholes
Jinxin Xue
In this paper we apply KAM theory and the Aubry-Mather theory for twist maps to the study of bound geodesic dynamics of a perturbed blackhole background. The general theories apply…
Lyapunov exponents for random perturbations of coupled standard maps
Alex Blumenthal, Jinxin Xue, Yun Yang
In this paper, we give a quantitative estimate for the sum of the first Lyapunov exponents for random perturbations of a natural class -dimensional volume-preserving system…
Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$
Sebastian Hurtado, Jinxin Xue
For groups of diffeomorphisms of $\T^2$ containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on $\T^2$ up to both t…
Rigidity of some abelian-by-cyclic solvable group actions on
Amie Wilkinson, Jinxin Xue
In this paper, we study a natural class of groups that act as affine transformations of . We investigate whether these solvable, "abelian-by-cyclic," groups can act sm…
Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits
Wenmin Gong, Jinxin Xue
We show that the existence of noncontractible periodic orbits for compactly supported time-dependent Hamiltonian on the disk cotangent bundle of a Finsler manifold provided that th…
Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
Alex Blumenthal, Jinxin Xue, Lai-Sang Young
We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A…
A C1 Arnol'd-Liouville theorem
Marie-Claude Arnaud, Jinxin Xue
In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori i…
Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom
Chong-Qing Cheng, Jinxin Xue
In this paper Arnold diffusion is proved to be a generic phenomenon in nearly integrable convex Hamiltonian systems with arbitrarily many degrees of freedom: $$ H(x,y)=h(y)+\eps P(…
Noncollision Singularities in a Planar Four-body Problem
Jinxin Xue
In this paper, we show that there is a Cantor set of initial conditions in the planar four-body problem such that all four bodies escape to infinity in a finite time, avoiding coll…
Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems
Jinxin Xue
In this paper, we show the existence of non contractible periodic orbits in Hamiltonian systems defined on $T^*\T^n$ separating two Lagrangian tori under certain cone assumption. O…
Non-Collision singularities in the Planar two-Center-two-Body problem
Jinxin Xue, Dmitry Dolgopyat
In this paper, we study a model of simplified four-body problem called planar two-center-two-body problem. In the plane, we have two fixed centers , of mass…
Continuous averaging proof of the Nekhoroshev theorem
Jinxin Xue
In this paper we develop the continuous averaging method of Treschev to work on the simultaneous Diophantine approximation and apply the result to give a new proof of the Nekhorosh…
Arnold Diffusion in a Restricted Planar Four-Body Problem
Jinxin Xue
This paper constructs a certain planar four-body problem which exhibits fast energy growth. The system considered is a quasi-periodic perturbation of the Restricted Planar Circular…