47 citations · 95 across the 21 of their papers we have counts for
16 papers · 1 filter
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…
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…
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,…
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…
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: $$ H(x,y)=h(y)+\eps P(…
Noncollision Singularities in a Planar Four-body Problem
Jinxin Xue
In this paper, we show that there is a Cantor set of initial conditions in the planar four-body problem such that all four bodies escape to infinity in a finite time, avoiding coll…
Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems
Jinxin Xue
In this paper, we show the existence of non contractible periodic orbits in Hamiltonian systems defined on $T^*\T^n$ separating two Lagrangian tori under certain cone assumption. O…
Non-Collision singularities in the Planar two-Center-two-Body problem
Jinxin Xue, Dmitry Dolgopyat
In this paper, we study a model of simplified four-body problem called planar two-center-two-body problem. In the plane, we have two fixed centers , of mass…
Continuous averaging proof of the Nekhoroshev theorem
Jinxin Xue
In this paper we develop the continuous averaging method of Treschev to work on the simultaneous Diophantine approximation and apply the result to give a new proof of the Nekhorosh…
Arnold Diffusion in a Restricted Planar Four-Body Problem
Jinxin Xue
This paper constructs a certain planar four-body problem which exhibits fast energy growth. The system considered is a quasi-periodic perturbation of the Restricted Planar Circular…
Arnold diffusion in nearly integrable Hamiltonian systems
Chong-Qing Cheng
In this paper, Arnold diffusion is proved to be generic phenomenon in nearly integrable convex Hamiltonian systems with three degrees of freedom: $$ H(x,y)=h(y)+εP(x,y), \qquad x\i…