Zhihong Xia

  • 532 Citations
1989 …2018

Research output per year

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Research Output

  • 532 Citations
  • 34 Article
  • 4 Chapter
  • 2 Conference contribution
2018

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

2 Scopus citations
2017

Homoclinic intersections for geodesic flows on convex spheres

Xia, Z. & Zhang, P., Jan 1 2017, Contemporary Mathematics. American Mathematical Society, p. 221-238 18 p. (Contemporary Mathematics; vol. 698).

Research output: Chapter in Book/Report/Conference proceedingChapter

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

2014

Homoclinic points for convex billiards

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

Research output: Contribution to journalArticle

4 Scopus citations
2013

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

3 Scopus citations
2012

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

11 Scopus citations
2010

Exponential Growth Rate of Paths and Its Connection with Dynamics

Xia, Z. & Zhang, P., 2010, Progress in Variational Methods. Liu, C. & Long, Y. (eds.). World Scientific Publishing Co. Pte Ltd, p. 212-224 13 p. (Nankai Series in Pure, Applied Mathematics and Theoretical Physics; vol. 7).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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

11 Scopus citations
2009

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

18 Scopus citations
2008

Symmetries in N-body problem

Zhihong, X., Oct 22 2008, Exploring the Solar System and the Universe. p. 126-132 7 p. (AIP Conference Proceedings; vol. 1043).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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

16 Scopus citations
2006

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

3 Scopus citations

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

9 Scopus citations

Area-Preserving Surface Diffeomorphisms

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

Research output: Contribution to journalArticle

9 Scopus citations

Generic Properties of Symplectic Diffeomorphisms: Fields Institute Communication 48

Saghin, R. & Xia, Z., 2006, Nonlinear Dynamics and Evolution Equations: Fields Institute Communication 48. Brunner, H., Zhao, X-Q. & Zou, X. (eds.). Providence: American Mathematical Society, p. 247-255

Research output: Chapter in Book/Report/Conference proceedingChapter

Hyperbolic Invariant Sets with Positive Measures

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

Research output: Contribution to journalArticle

5 Scopus citations

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

20 Scopus citations
2005

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

3 Scopus citations
2004

Convex central congurations for the n-body problem

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

Research output: Contribution to journalArticle

28 Scopus citations
2003

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

1 Scopus citations

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

1 Scopus citations
2000

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

53 Scopus citations

Homoclinic points and intersections of Lagrangian submanifolds

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

Research output: Contribution to journalArticle

4 Scopus citations
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

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

4 Scopus citations
1998

Bifurcations of heteroclinic loops

Zhu, D. & Xia, Z., Dec 1 1998, In : Science in China, Series A: Mathematics, Physics, Astronomy. 41, 8, p. X6-848 12 p.

Research output: Contribution to journalArticle

59 Scopus citations

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

2 Scopus citations

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

Homoclinic points in symplectic and volume-preserving diffeomorphisms

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

Research output: Contribution to journalArticle

29 Scopus citations
1995

Arnold diffusion with degenracies in Hamiltonian systems: Vol. 1: Mathematics, Economics, and Engineering

Xia, Z., 1995, Dynamical Systems and Chaos: Vol. 1: Mathematics, Economics, and Engineering. Aoki, N. & Takahashi, Y. (eds.). River Edge, NJ: World Scientific Publishing Company, p. 278-285

Research output: Chapter in Book/Report/Conference proceedingChapter

Existence of invariant tori for certain non-symnplectic diffeomorphisms: The IMA Volumes in Mathematics and Its Application

Xia, Z., 1995, Hamiltonian Dynamical Systems: History, Theory, and Applications: The IMA Volumes in Mathematics and Its Application. Dumas, H. S., Meyer, K. R. & Schmidt, D. S. (eds.). New York: Springer-Verlag, p. 373-385

Research output: Chapter in Book/Report/Conference proceedingChapter

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

28 Scopus citations

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 Scopus citations
1993
17 Scopus citations
1992

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

67 Scopus citations
40 Scopus citations

The existence of noncollision singularities in Newtonian systems

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

Research output: Contribution to journalArticle

1991

Central configurations with many small masses

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

Research output: Contribution to journalArticle

40 Scopus citations
1989

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

16 Scopus citations