段华贵

• 性别：男

  职称：教授

  所在系别：基础数学系

  是否博导：是

• 办公地点：吉林大学中心校区，伍卓群楼

  电子邮箱：duanhg@jlu.edu.cn

• 非线性分析、哈密顿系统与辛几何

• 本科生课程：《数学分析》、《实变函数》、《数理方程》、《线性代数》等
  研究生课程：《常微分方程》、《微分几何》、《非线性泛函分析》、《辛几何与辛拓扑》等

• 2004.09 - 2007.06 南开大学陈省身数学研究所 博士研究生
  2001.09 - 2004.06 江西师范大学数学与统计学院 硕士研究生
  1996.09 - 1999.06 九江学院（原九江师专）数学系

• 2026.05 - 至今 吉林大学数学学院 教授
  2016.12 - 2026.05 南开大学数学科学学院 教授
  2009.12 - 2016.12 南开大学数学科学学院 副教授
  2007.07-2009.12 南开大学数学科学学院 讲师

• 1. 辛拓扑和混沌动力学，2024.01-2026.12，国家自然科学基金委国际合作与交流项目，参与人
  2. 动力系统的周期轨道与测地流的研究，2023.01-2026.12，国家自然科学基金面上项目，负责人
  3. 哈密顿系统周期轨道与辛几何相关问题，2020.12-2025.11，科技部国家重点研发计划（课题），参与人
  4. 哈密顿系统的周期轨道和辛映射的不动点研究，2018.01-2022.12，国家自然科学基金重大项目（课题），参与人
  5. 哈密顿动力系统周期轨道的多重性与稳定性研究，2017.01-2020.12，国家自然科学基金面上项目，负责人
  6. Hamilton系统周期运动轨道的研究，2012.01-2016.12，国家自然科学基金重点项目，参与人
  7. 流形上的闭测地线与哈密顿系统中的闭特征，2009.01-2011.12，国家自然科学基金青年科学基金项目（C类），负责人

• [1] Duan, Huagui; Xie, Dong, Multiple closed characteristics on compact star-shaped hypersurface. Trans. Amer. Math. Soc. 379 (2026)，no. 7,4925-4944.
  [2] Duan, Huagui; Xie, Dong, Multiple closed geodesics on a sphere of odd dimension, J. Differential Geom. 133 (2026), no. 1, 1–13.
  [3] Duan, Huagui; Fan, Zhiping，Multiple closed characteristics on compact star-shaped hypersurfaces in R10. J. Differential Equations, 465 (2026), Paper No. 114207, 31 pp.
  [4] Duan, Huagui; Xie, Dong，On the minimal number of closed geodesics on positively curved Finsler spheres. J. Reine Angew. Math. 830 (2026), 259–283.
  [5] Duan, Huagui; Xie, Dong，Four closed characteristics on compact star-shaped hypersurfaces in R8. J. Geom. Anal. 35 (2025), no. 10, Paper No. 289, 14 pp.
  [6] Duan, Huagui; Liu, Hui; Long, Yiming; Qi, Zihao; Wang, Wei,Three closed characteristics on non-degenerate star-shaped hypersurfaces in R6.J. Differential Equations, 446 (2025), Paper No. 113605, 30 pp.
  [7] Duan, Huagui; Qi, Zihao，Multiple closed geodesics on Finsler 3-dimensional sphere. J. Funct. Anal. 288 (2025), no. 10, Paper No. 110863, 17 pp.
  [8] Duan, Huagui; Liu, Hui; Long, Yiming; Wang, Wei，Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond. J. Funct. Anal. 286 (2024), no. 7, Paper No. 110352, 41 pp.
  [9] Duan, Huagui; Xie, Dong，Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics. J. Funct. Anal. 284 (2023), no. 8, Paper No. 109861, 20 pp.
  [10] Duan, Huagui; Liu, Hui; Ren, Wenyan，A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in R2n. Math. Z. 302 (2022), no. 2, 743–757.
  [11] Duan, Hua Gui; Liu, Hui, The non-contractibility of closed geodesics on Finsler RPn. Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 1, 1–21.
  [12] Duan, Huagui; Long, Yiming; Zhu, Chaofeng，Index iteration theories for periodic orbits: old and new. Nonlinear Anal. 201 (2020), 111999, 26 pp.
  [13] Duan, Huagui; Liu, Hui; Long, Yiming; Wang, Wei, Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in R2n. Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 1, 1–18.
  [14] Duan, Huagui；Liu,Hui, Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in R2n. Calc. Var. Partial Differential Equations, 56 (2017), no. 3, Paper No. 65, 30 pp.
  [15] Duan, Huagui; Long, Yiming; Wang, Wei,The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds. Calc. Var. Partial Differential Equations, 55 (2016), no. 6, Art. 145, 28 pp.
  [16] Duan, Huagui; Long, Yiming; Wang, Wei，Two closed geodesics on compact simply connected bumpy Finsler manifolds. J. Differential Geom. 104 (2016), no. 2, 275–289.
  [17] Duan, Huagui，Two elliptic closed geodesics on positively curved Finsler spheres. J. Differential Equations, 260 (2016), no. 12, 8388–8402.
  [18] Duan, Huagui; Liu, Hui, Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics. Sci. China Math. 59 (2016), no. 3, 531–538.
  [19] Duan, Huagui; Liu, Hui, Closed geodesics on positively curved Finsler 3-spheres. Adv. Nonlinear Stud. 16 (2016), no. 1, 159–171.
  [20] Duan, Huagui; Long, Yiming; Xiao, Yuming，Two closed geodesics on RP2n+1 with a bumpy Finsler metric. Calc. Var. Partial Differential Equations, 54 (2015), no. 3, 2883–2894.
  [21] Duan, Huagui，Non-hyperbolic closed geodesics on positively curved Finsler spheres. J. Funct. Anal. 269 (2015), no. 11, 3645–3662.
  [22] Duan, Huagui; Liu, Hui, The irrational ratio of average indices of closed geodesics on positively curved Finsler spheres. Nonlinear Anal. 128 (2015), 36–47.
  [23] Duan, Huagui；Long,Yiming, The index growth and multiplicity of closed geodesics. J. Funct. Anal. 259 (2010), no. 7, 1850–1913.
  [24] Long, Yiming; Duan, Huagui，Multiple closed geodesics on 3-spheres. Adv. Math. 221 (2009), no. 6, 1757–1803.
  [25] Duan, Huagui; Long, Yiming, Morse concavity for closed geodesics. Acta Math. Sci. Ser. B (Engl. Ed.) 29 (2009), no. 3, 731–750.
  [26] Duan, Huagui; Long, Yiming，Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres. Calc. Var. Partial Differential Equations， 31 (2008), no. 4, 483–496.
  [27] Duan, Huagui; Long, Yiming，Multiple closed geodesics on bumpy Finsler n-spheres. J. Differential Equations, 233 (2007), no. 1, 221–240.

• 1. 2026年，入选国家级人才项目
  2. 2025年，《数学分析I》入选第三批国家一流本科课程（本人排序2）
  3. 2021年，第六届中国科协优秀科技论文
  4. 2018年，入选南开大学百名青年学科带头人计划
  5. 2017年，天津市数学会青年学术奖一等奖
  6. 2010年，第十届天津市高校青年教师教学基本功竞赛理科类一等奖