Zhihong Xia

  • 574 Citations
1989 …2018
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Research Output 1989 2018

  • 574 Citations
  • 35 Article
  • 4 Chapter
  • 2 Conference contribution
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Article
2018
2 Citations (Scopus)

Conley-Zehnder index and bifurcation of fixed points of Hamiltonian maps

Deng, Y. & Xia, Z., Sep 1 2018, In : Ergodic Theory and Dynamical Systems. 38, 6, p. 2086-2107 22 p.

Research output: Contribution to journalArticle

Hamiltonians
Bifurcation (mathematics)
Bifurcation
Fixed point
Nondegeneracy
2016

Minimal measures for Euler-Lagrange flows on finite covering spaces

Wang, F. & Xia, Z., Oct 14 2016, In : Nonlinearity. 29, 12, p. 3625-3646 22 p.

Research output: Contribution to journalArticle

Covering Space
Lagrange
Euler
coverings
Fundamental Group
2014
4 Citations (Scopus)

Homoclinic points for convex billiards

Xia, Z. & Zhang, P., Jan 1 2014, In : Nonlinearity. 27, 6, p. 1181-1192 12 p.

Research output: Contribution to journalArticle

Homoclinic Point
Generic Property
Homoclinic Orbit
Periodic Points
Billiards
2013
3 Citations (Scopus)

Stability of Elliptic Periodic Points with an Application to Lagrangian Equilibrium Solutions

Hua, Y. & Xia, Z., Apr 15 2013, In : Qualitative Theory of Dynamical Systems. 12, 1, p. 243-253 11 p.

Research output: Contribution to journalArticle

Equilibrium Solution
Nonlinear Stability
Periodic Points
Degree of freedom
Linear Stability
2012
10 Citations (Scopus)

Action-minimizing periodic and quasi-periodic solutions in the N-body problem

Chen, K. C., Ouyang, T. & Xia, Z., Jan 1 2012, In : Mathematical Research Letters. 19, 2, p. 483-497 15 p.

Research output: Contribution to journalArticle

N-body Problem
Quasi-periodic Solutions
Braid
Collision
Reflectional symmetry
2010
9 Citations (Scopus)

The Entropy Conjecture for Partially Hyperbolic Diffeomorphisms with 1-D Center

Saghin, R. & Xia, Z., 2010, In : Topology and its Applications. 157, p. 29

Research output: Contribution to journalArticle

2009
17 Citations (Scopus)

Geometric expansion, Lyapunov exponents and foliations

Saghin, R. & Xia, Z., Jan 1 2009, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 26, 2, p. 689-704 16 p.

Research output: Contribution to journalArticle

Foliation
Lyapunov Exponent
Topological Invariants
Center Manifold
Diffeomorphisms
2008
15 Citations (Scopus)

Topological Entropy and Partially Hyperbolic Diffeomorphisms

Hua, Y., Saghin, R. & Xia, Z., 2008, In : Ergodic Theory and Dynamical Systems. 28, p. 843

Research output: Contribution to journalArticle

2006
3 Citations (Scopus)

A C^r closing lemma for a class of sym- plectic dieomorphisms

Xia, Z., 2006, In : Nonlinearity. 19, p. 511

Research output: Contribution to journalArticle

9 Citations (Scopus)

Area-preserving surface diffeomorphisms

Xia, Z., May 1 2006, In : Communications in Mathematical Physics. 263, 3, p. 723-735 13 p.

Research output: Contribution to journalArticle

Diffeomorphisms
preserving
Generic Property
Unstable Manifold
unions
9 Citations (Scopus)

Area-Preserving Surface Diffeomorphisms

Xia, Z., 2006, In : Communications in Mathematical Physics. 263, p. 723

Research output: Contribution to journalArticle

5 Citations (Scopus)

Hyperbolic Invariant Sets with Positive Measures

Xia, Z., 2006, In : Discrete and Continuous Dynamical Systems. 15, p. 811

Research output: Contribution to journalArticle

20 Citations (Scopus)

Partial hyperbolicity or dense elliptic periodic points for C 1-generic symplectic diffeomorphisms

Saghin, R. & Xia, Z., Nov 1 2006, In : Transactions of the American Mathematical Society. 358, 11, p. 5119-5136 18 p.

Research output: Contribution to journalArticle

Partial Hyperbolicity
Periodic Points
Diffeomorphisms
Diffeomorphism
Ergodicity
2005
3 Citations (Scopus)

Non-planar minimizers and rotational symmetry in the N-body problem.

Salomone, M. & Xia, Z., 2005, In : Journal of Differential Equations. 215, p. 1

Research output: Contribution to journalArticle

2004
27 Citations (Scopus)

Convex central congurations for the n-body problem

Xia, Z., 2004, In : Journal of Differential Equations. 200, p. 185

Research output: Contribution to journalArticle

2003
1 Citation (Scopus)

Heteroclinic orbits and chaotic invariant sets for monotone twist maps

Qian, T. & Xia, Z., Jan 1 2003, In : Discrete and Continuous Dynamical Systems. 9, 1, p. 69-95 27 p.

Research output: Contribution to journalArticle

Twist Map
Monotone Map
Heteroclinic Orbit
Invariant Set
Orbits
1 Citation (Scopus)

Heteroclinic Orbits and Chaotic Invariant Sets for Monotone Twist Maps

Qian, T. & Xia, Z., 2003, In : Discrete and Continuous Dynamical Systems. 9, p. 69

Research output: Contribution to journalArticle

2000
51 Citations (Scopus)

C1 connecting lemmas

Wen, L. & Xia, Z., Dec 1 2000, In : Transactions of the American Mathematical Society. 352, 11, p. 5213-5230 18 p.

Research output: Contribution to journalArticle

Lemma
Dynamical systems
Hyperbolic Set
Stable and Unstable Manifolds
Invariant Set
4 Citations (Scopus)

Homoclinic points and intersections of Lagrangian submanifolds

Xia, Z., 2000, In : Discrete and Continuous Dynamical Systems. 6, p. 243

Research output: Contribution to journalArticle

Homoclinic Point
Intersection Theory
Hamiltonians
Stable and Unstable Manifolds
Lagrangian Submanifold
1999

A basic C^1 perturbation theorem

Wen, L. & Xia, Z., 1999, In : Journal of Differential Equations. 154, p. 267

Research output: Contribution to journalArticle

4 Citations (Scopus)

A basic C1 perturbation theorem

Wen, L. & Xia, Z., May 20 1999, In : Journal of Differential Equations. 154, 2, p. 267-283 17 p.

Research output: Contribution to journalArticle

Perturbation
Theorem
Lemma
1998
57 Citations (Scopus)

Bifurcations of heteroclinic loops

Zhu, D. & Xia, Z., 1998, In : Science in China Series A: Mathematics. 41, p. 837

Research output: Contribution to journalArticle

57 Citations (Scopus)

Bifurcations of heteroclinic loops

Zhu, D. & Xia, Z., Dec 1 1998, In : Science in China, Series A: Mathematics, Physics, Astronomy. 41, 8

Research output: Contribution to journalArticle

Bifurcation
Orbit
Unproved
Exponential Dichotomy
Periodic Systems
2 Citations (Scopus)

Instability and Diffusion in the Elliptic Restricted Three-Body Problem

Liao, X., Saari, D. G. & Xia, Z., Jan 1 1998, In : Celestial Mechanics and Dynamical Astronomy. 70, 1, p. 23-39 17 p.

Research output: Contribution to journalArticle

three body problem
orbits
indication
celestial mechanics
mechanics

Instability and diusion in the elliptic restricted three-body problem

Liao, X., Saari, D. G. & Xia, Z., 1998, In : Celestial Mechanics and Dynamical Astronomy. 70, p. 23

Research output: Contribution to journalArticle

1996
29 Citations (Scopus)

Homoclinic points in symplectic and volume-preserving diffeomorphisms

Xia, Z., 1996, In : Communications in Mathematical Physics. 177, p. 435

Research output: Contribution to journalArticle

1995
28 Citations (Scopus)

Off to infinity in finite time

Saari, D. G. & Xia, Z., 1995, In : Notices of the American Mathematical Society. 42, p. 538

Research output: Contribution to journalArticle

Subharmonic solutions in the restricted three-body problem

Cabral, H. E. & Xia, Z., 1995, In : Discrete and Continuous Dynamical Systems. 1, p. 463

Research output: Contribution to journalArticle

1994
29 Citations (Scopus)
1993
17 Citations (Scopus)
1992
63 Citations (Scopus)

Existence of invariant tori in volume-preserving diffeomorphisms

Xia, Z., 1992, In : Ergodic Theory and Dynamical Systems. 12, p. 621

Research output: Contribution to journalArticle

39 Citations (Scopus)

The existence of noncollision singularities in Newtonian systems

Xia, Z., 1992, In : Annals of Mathematics. 2, p. 411

Research output: Contribution to journalArticle

1991
40 Citations (Scopus)

Central configurations with many small masses

Xia, Z., 1991, In : Journal of Differential Equations. 91, p. 168

Research output: Contribution to journalArticle

1989
16 Citations (Scopus)

The existence of oscillatory and superhyperbolic motion in Newtonian systems

Saari, D. G. & Xia, Z., 1989, In : Journal of Differential Equations. 82, p. 342

Research output: Contribution to journalArticle