研究领域：动力系统与非线性分析的研究，侧重于研究有物理背景的数学问题。在哈密顿系统指标理
        论，N体问题，稳定性问题及哈密顿微分算子的谱问题等方面取得系列进展。

  电话：0531-88363959

  邮箱：xjhu@sdu.edu.cn

1999-9 — 2002-6：南开大学基础数学博士

1997-9 — 1999-6：吉林大学基础数学硕士

1993-9 — 1997-6：吉林大学数学学士

2002-7 — 2008-6：中科院数学院

2008-6-至今：山东大学数学院

2005：2004国家自然科学二等奖（第四完成人）；

2013：教育部“新世纪优秀人才支持计划“入选者；

2014： 国家杰出青年科学基金获得者；

2018：政府特殊津贴；

2019：山东省有突出贡献的中青年专家；

2023：2022教育部高等学校科学研究优秀成果奖（科学技术）一等奖（首位）

 

 

1. Linear Stability of an Elliptic Relative Equilibrium in the Spatial n-Body Problem via Index Theory.  REGULAR & CHAOTIC DYNAMICS,  2023.

 

2. On the jth Eigenvalue of Sturm-Liouville Problem and the Maslov Index.  Journal of Dynamics and Differential Equations,  34,  1949, 2022.

 

3. Mean Index for Non-periodic Orbits in Hamiltonian Systems.  38,  291-310, 2022.

 

4. Hill-Type Formula and Krein-Type Trace Formula for Hamiltonian Systems.  Analysis in Theory and Applications,  37,  74, 2021.

 

5. DECOMPOSITION OF SPECTRAL FLOW AND BOTT-TYPE ITERATION FORMULA.  ELECTRONIC RESEARCH ARCHIVE,  28,  127, 2020.

 

6. An index theory for asymptotic motions under singular potentials.  Advances in Mathematics,  370,  2020.

 

7. Hill-type formula and Krein-type trace formula for S-periodic solutions in ODEs.  Discrete and Continuous Dynamical Systems,  36,  763, 2016.

 

8. Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit.  Journal of Dynamics and Differential Equations,  32,  61, 2020.

 

9. Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions.  MATHEMATISCHE ZEITSCHRIFT,  283,  339, 2016.

 

10. Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions.  Archive for Rational Mechanics and Analysis,  216,  313, 2015.

 

11. An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian n-body Problem.  ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,  240,  565, 2021.

 

11. An Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem.  Communications in Mathematical Physics,  361,  709, 2018.

 

13. On the jth Eigenvalue of Sturm-Liouville Problem and the Maslov Index.  Journal of Dynamics and Differential Equations,  34,  1949, 2022.

 

14. Mean Index for Non-periodic Orbits in Hamiltonian Systems.  38,  291-310, 2022.

 

15.Hu, Xijun , Ou,yuwei  and Yu, Guowei. An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian n-body Problem.  ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,  240,  565, 2021.

 

16. Hu, Xijun , Ou, Yuwei , Wang, Penghui  and Zhu, Hao. Hill-Type Formula and Krein-Type Trace Formula for Hamiltonian Systems.  Analysis in Theory and Applications,  37,  74, 2021.

 

17. Barutello, Vivina L. , Hu, xijun , Portaluri, Alessandro  and Terracini, Susanna. An index theory for asymptotic motions under singular potentials.  Advances in Mathematics,  370,  2020.

 

18. Hu, Xijun , Portaluri, A.  and Xing, Qin. Morse Index and Stability of the Planar N-vortex Problem.  QUALITATIVE THEORY OF DYNAMICAL SYSTEMS,  19,  2020.

 

19. 胡锡俊 , 吴立  and 杨冉. Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit.  Journal of Dynamics and Differential Equations,  32,  61, 2020.

 

20. Hu, Xijun , Long, Yiming  and Ou, Yuwei. Linear stability of the elliptic relative equilibrium with (1+n)-gon central configurations in planar n-body problem.  Nonlinearity,  33,  1016, 2020.

 

21. Hu, Xijun  and Wu, Li. DECOMPOSITION OF SPECTRAL FLOW AND BOTT-TYPE ITERATION FORMULA.  ELECTRONIC RESEARCH ARCHIVE,  28,  127, 2020.

 

22. Hu, Xijun , Portaluri, Alessandro  and Yang, Ran. A dihedral Bott-type iteration formula and stability of symmetric periodic orbits.  CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Journal,  59,  2020.

 

23. 胡锡俊 , Portaluri, Alessandro  and Yang, Ran. Instability of semi-Riemannian closed geodesics.  Nonlinearity,  32,  4281, 2019.

 

24. 胡锡俊 , 欧昱伟  and 王鹏辉. Hill-type formula for Hamiltonian system with Lagrangian boundary conditions.  JOURNAL OF DIFFERENTIAL EQUATIONS,  267,  2416, 2019.

 

25. 胡锡俊  and Portaluri, Alessandro. Bifurcation of heteroclinic orbits via an index theory.  MATHEMATISCHE ZEITSCHRIFT,  292,  705, 2019.

 

26. 胡锡俊 , Liu, Lei , 吴立  and Zhu,hao. Singularity of the n-th eigenvalue of high dimensional Sturm-Liouville problems.  JOURNAL OF DIFFERENTIAL EQUATIONS Journal,  266,  4106, 2019.

 

27. 胡锡俊  and Yu, guowei. An Index Theory for Zero Energy Solutions of the Planar Anisotropic Kepler Problem.  Communications in Mathematical Physics,  361,  709, 2018.

 

28. 胡锡俊  and Portaluri, A.. Index theory for heteroclinic orbits of Hamiltonian systems.  Calculus of Variations and Partial Differential Equations,  56,  2017.

 

29. 胡锡俊  and 欧昱伟. Stability of closed characteristics on compact convex hypersurfaces in R^2n.  Journal of Fixed Point Theory and Applications,  19,  585, 2017.

 

30. 胡锡俊. Collision Index and Stability of Elliptic Relative Equilibria in Planar -body Problem..  Communications in Mathematical Physics,  2016.

 

31. 胡锡俊  and 王鹏辉. Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions.  MATHEMATISCHE ZEITSCHRIFT,  283,  339, 2016.

 

32. 胡锡俊  and 王鹏辉. Hill-type formula and Krein-type trace formula for S-periodic solutions in ODEs.  Discrete and Continuous Dynamical Systems,  36,  763, 2016.

 

33. 胡锡俊 , 欧昱伟  and 王鹏辉. Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions.  Archive for Rational Mechanics and Analysis,  216,  313, 2015.

 

34. 胡锡俊 , Long, Yiming  and Sun, Shanzhong. Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory.  Archive for Rational Mechanics and Analysis,  2014.

 

35. 胡锡俊  and 欧昱伟. An Estimation for the Hyperbolic Region of Elliptic Lagrangian solutions in the planar three-body problem.  Regular and Chaotic Dynamics,  18,  732, 2013.

 

36. 胡锡俊  and 王鹏辉. Conditional Fredholm Determinant and Trace formula for Hamiltonian Systems: a Survey. .  Nankai Series in Pure, Applied Mathematics and Theoretical physics,  10,  12, 2013.

 

37. 胡锡俊  and 欧昱伟. Stability analysis for standing pulse solutions to FitzHugh–Nagumo equations.  Calculus of Variations and Partial Differential Equations,  2013.

 

38. 胡锡俊  and 王鹏辉. Conditional Fredholm determinant for the S-periodic orbits in Hamiltonian systems.  Journal of Functional Analysis,  261,  3247, 2011.

 

39. 胡锡俊  and Sun, Shanzhong. Variational principle and linear stability of periodic orbits in celestial mechanics.  Nankai Series in Pure, Applied Mathematics and Theoretical Physics, Progress in Variational Methods,  7,  40, 2010.

 

40. 胡锡俊  and Sun, Shanzhong. Morse Index and the Stability of Closed Geodesics.  SCIENCE CHINA Mathematics,  53,  1207, 2010.

 

41. 胡锡俊  and Sun, Shanzhong. Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem.  Advances in Mathematics,  223,  98, 2010.

 

42. 胡锡俊  and Sun, Shanzhong. Stability of relative equilibria and Morse index of central configurations.  COMPTES RENDUS MATHEMATIQUE,  347,  1309, 2009.

 

43. 胡锡俊  and Sun, Shanzhong. Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit.  Communications in Mathematical Physics,  290,  737, 2009.

 

1. 天体力学-N体问题, 2020/11/30-2025/11/30

 

2. 哈密顿系统中奇性轨道的研究, 2020/09/18-2024/12/31

 

3. 天体力学-N 体问题, 科技部重点研发课题