研究领域为拓扑动力系统与遍历理论，主要研究内容包括动力系统复杂性理论及其在组合数论、微分方程中的应用。(The research field is topological dynamical systems and ergodic theory, with main research contents including the complexity theory of dynamical systems and its applications in combinatorial number theory and differential equations.)

arxiv: [2411.03512] Ergodicity and Mixing of Sublinear Expectation System and Applications

     [2411.02030] Finite ergodic components for upper probabilities

     [2411.00663] Ergodicity and Mixing of invariant capacities and applications

     [2409.07979] Multiple recurrence without commutativity

     [2408.11661] Some Extensions of Finite Sum Theorem 

     [2407.10728] A counterexample on multiple convergence without commutativity

     [2311.05193] Observable full-horseshoes for Lagrangian flows advected by stochastic 2D Navier-Stokes equations

             [2310.16780] Pointwise convergence of some continuous-time polynomial ergodic averages

     [2303.05027] Full-horseshoes for the Galerkin truncations of 2D Navier-Stokes equation with degenerate stochastic forcing

              [2301.07881] Polynomial Furstenberg joinings and its applications

             [2301.07873] Topological dynamical systems induced by polynomials and combinatorial consequences

     [1904.10608] Ergodic optimization theory for Axiom A flows

     [1904.01915] Ergodic optimization theory for a class of typical maps

1.接受待发表论文(Accepted papers)

98.Glasner, Eli；Huang, Wen; Shao, Song; Weiss, Benjamin; Ye, Xiangdong. Topological characteristic factors and nilsystems. J. Eur. Math. Soc., accepted.

 DOI 10.4171/JEMS/1379

97. Huang, Wen; Lian Zeng; Lu, Kening. Dynamical complexity of Anosov systems driven by a quasi-periodic force.  Sci. China Math., accepted. 

https://doi.org/10.1007/s11425-023-2207-x

96. Huang, Wen; Wang, Jin; Wang, Zhiren; Zhou, Qi. Quantitative Almost Reducibility and Möbius Disjointness for Analytic Quasiperiodic Schrödinger Cocycles. Peking Math. J., accepted.

https://doi.org/10.1007/s42543-023-00081-5

2.发表的论文(Published papers) 

95.Huang, Wen; Ma, Xiao; Xu, Leiye. Semi-horseshoe, entropy, and partial hyperbolicity. Adv. Math. 453 (2024), Paper No. 109849, 41 pp.

94.Goswami, Sayan;  Huang, Wen; Wu, XiaoSheng.  On the set of Kronecker numbers.   Bull. Aust. Math. Soc.  110 (2024), 262-270 .

93. Huang, Wen; Xu, Leiye; Ye, Xiangdong. Polynomial mean complexity and logarithmic Sarnak conjecture. Ergodic Theory Dynam. Systems 44 (2024), no. 3, 769-798.

92.Huang, Wen; Shao, Song; Ye, Xiangdong A counterexample on polynomial multiple convergence without commutativity. Bull. Soc. Math. France 152 (2024), no. 1, 149-168.

91. Huang, Wen; Liu, Xue; Ma, Xiao. Random semi-horseshoe for partially hyperbolic systems driven by an external force.  Physica Scripta, 98(2023), 085221.

90. Huang, Wen; Shao, Song; Ye, Xiangdong. Parallels between topological dynamics and ergodic theory. Ergodic theory, 389-426, Encycl. Complex. Syst. Sci., Springer, New York, [2023], ©2023.

89. Huang, Wen; Shao, Song; Ye, Xiangdong. Multiply minimal points for the product of iterates. Israel J. Math. 251 (2022), no. 2, 541-565.

88.Huang, Wen; Lian, Zeng. Horseshoes for Anosov Systems on Fibers Driven by an Equicontinuous System. Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 1, 281–290.

87.Huang, Wen; Wei, Run Ju; Yu, Tao; Zhou, Xiao Min. Measure Complexity and Rigid Systems. Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 1, 68–84.

86. Feng, Shilin; Gao, Rui; Huang, Wen; Lian, Zeng. Local stable and unstable sets for positive entropy C1 dynamical systems. Sci. China Math. 65 (2022), no. 1, 63–80.

85. Huang, Wen; Li, Jian; Ye, Xiangdong Positive entropy implies chaos along any infinite sequence. Trans. Moscow Math. Soc. 82 (2021), 1-14.

84.Huang, Wen; Li, Jian; Xu, Leiye; Ye, Xiangdong. The existence of semi-horseshoes for partially hyperbolic diffeomorphisms. Adv. Math. 381 (2021), Paper No. 107616, 23 pp.

83. Huang, Wen; Lian, Zhengxing; Shao, Song; Ye, Xiangdong. Minimal systems with finitely many ergodic measures. J. Funct. Anal. 280 (2021), no. 12, Paper No. 109000, 42 pp.

82. Huang, Wen; Li, Jian; Thouvenot, Jean-Paul; Xu, Leiye; Ye, Xiangdong. Bounded complexity, mean equicontinuity and discrete spectrum. Ergodic Theory Dynam. Systems 41 (2021), no. 2, 494–533.

81. Huang, Wen; Liu, Jianya; Wang, Ke. Möbius disjointness for skew products on a circle and a nilmanifold. Discrete Contin. Dyn. Syst. 41 (2021), no. 8, 3531–3553.

80. Huang, Wen; Xu, Leiye; Xu, Shengnan. Ergodic measures of intermediate entropy for affine transformations of nilmanifolds. Electron. Res. Arch. 29 (2021), no. 4, 2819–2827.

79. Glasner, Eli; Huang, Wen; Shao, Song; Ye, Xiangdong. Regionally proximal relation of order d along arithmetic progressions and nilsystems. Sci. China Math. 63 (2020), no. 9, 1757–1776.

78. Huang, Wen; Shao, Song; Ye, Xiangdong. An answer to Furstenberg's problem on topological disjointness. Ergodic Theory Dynam. Systems 40 (2020), no. 9, 2467–2481.

77. Huang, Wen; Xu, Leiye; Ye, Xiangdong. A minimal distal map on the torus with sub-exponential measure complexity. Ergodic Theory Dynam. Systems 40 (2020), no. 4, 953–974.

76. Huang, Wen; Qian, Hong; Wang, Shirou; Ye, Felix X.; Yi, Yingfei. Synchronization in discrete-time, discrete-state random dynamical systems. SIAM J. Appl. Dyn. Syst. 19 (2020), no. 1, 233–251.

75. Huang, Wen; Shao, Song; Ye, Xiangdong. Pointwise convergence of multiple ergodic averages and strictly ergodic models. J. Anal. Math. 139 (2019), no. 1, 265–305.

74. Huang, Wen; Shao, Song; Ye, Xiangdong. Topological correspondence of multiple ergodic averages of nilpotent group actions. J. Anal. Math. 138 (2019), no. 2, 687-715.

73. Huang, Wen; Wang, Zhiren; Zhang, Guohua. Möbius disjointness for topological models of ergodic systems with discrete spectrum. J. Mod. Dyn. 14(2019), 277-290.

72. Dou, Dou; Huang, Wen; Park, Kyewon Koh. Entropy dimension of measure preserving systems. Trans. Amer. Math. Soc.  371 (2019), no. 10, 7029-7065.

71. Huang, Wen; Wang, Zhiren; Ye, Xiangdong. Measure complexity and Möbius disjointness. Adv. Math.  347(2019), 827-858.

70. Huang, Wen; Xu, Leiye. Special flow, weak mixing and complexity. Commun. Math. Stat. 7(2019), no. 1, 85-122.

69.Huang, Wen; Khilko, Danylo; Kolyada, Sergiĭ; Peris, Alfred; Zhang, Guohua. Finite intersection property and dynamical compactness. J. Dynam. Differential Equations 30 (2018), no. 3, 1221-1245.

68. Huang, Wen; Kolyada, Sergiĭ; Zhang, Guohua. Analogues of Auslander-Yorke theorems for multi-sensitivity. Ergodic Theory Dynam. Systems 38 (2018),   no. 2, 651-665.

67. Huang,Wen; Ji,Min; Liu, Zhenxin; Yi, Yingfei. Concentration and limit behaviors of stationary measures. Phys. D 369 (2018), 1-17.

66. Gutman,Yonatan; Huang, Wen; Shao, Song; Ye, Xiangdong. Almost sure convergence of the multiple ergodic average for certain weakly mixing systems. Acta Math. Sin. (Engl. Ser.)  34(2018), no. 1, 79-90.

65.Huang, Wen; Lu, Kening. Entropy, chaos, and weak horseshoe for infinite-dimensional random dynamical systems. Comm. Pure Appl. Math.  70 (2017), no. 10, 1987-2036.

64. Huang, Wen; Wu, XiaoSheng. On the set of the difference of primes. Proc. Amer. Math. Soc.  145 (2017), no. 9, 3787-3793.

63. Huang, Wen; Lian, Zhengxing; Shao, Song; Ye, Xiangdong. Sequences from zero entropy noncommutative toral automorphisms and Sarnak conjecture. J. Differential Equations 263 (2017), no. 1, 779-810.

62. Huang, Wen; Shao, Song; Ye, Xiangdong. Strictly ergodic models under face and parallelepiped group actions. Commun. Math. Stat.  5 (2017), no. 1, 93-122.

61. Huang, Wen; Li, Jian; Ye, Xiangdong; Zhou, Xiaoyao. Positive topological entropy and Δ-weakly mixing sets. Adv. Math.  306 (2017), 653-683.

60. Huang, Wen; Jin, Lei. Stable sets and mean Li-Yorke chaos in positive entropy actions of bi-orderable amenable groups. Ergodic Theory Dynam. Systems 36 (2016),  no. 8, 2482-2497.

59. Huang, Wen; Zhou, Xiaomin. Recurrent sets, entropy and independence.  Dynamics and numbers, 123-136, Contemp. Math., 669, Amer. Math. Soc., Providence, RI, 2016.

58. Huang, Wen; Jin, Lei; Ye, Xiangdong. On extensions over semigroups and applications. Entropy 18 (2016), no. 6, Paper No. 230, 6 pp.

57. Feng, De-Jun; Huang, Wen. Variational principle for weighted topological pressure. J. Math. Pures Appl. (9) 106(2016), no. 3, 411-452.

56. Che, Rui; Huang, Wen; Li, Yao; Tetali, Prasad. Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities. J. Differential Equations 261(2016), no. 4, 2552-2583.

55. Huang, Wen; Shao, Song; Ye, Xiangdong. Nil Bohr-sets and almost automorphy of higher order. Mem. Amer. Math. Soc. 241(2016), no. 1143, v+83 pp.

54. Foryś, Magdalena; Huang, Wen; Li, Jian; Oprocha, Piotr. Invariant scrambled sets, uniform rigidity and weak mixing. Israel J. Math.  211 (2016), no. 1, 447–472.

53. Huang, Wen; Khilko, Danylo; Kolyada, Sergiĭ; Zhang, Guohua. Dynamical compactness and sensitivity. J. Differential Equations 260 (2016), no. 9, 6800-6827.

52. Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei. Steady states of Fokker-Planck equations: III. Degenerate diffusion. J. Dynam. Differential Equations 28 (2016), no. 1, 127-141.

51. Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei. Stochastic stability of measures in gradient systems. Phys. D 314 (2016), 9-17.

50．Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei. Steady states of Fokker-Planck equations: II. Non-existence. J. Dynam. Differential Equations 27 (2015), no. 3-4, 743-762.

49. Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei. Steady states of Fokker-Planck equations: I. Existence. J. Dynam. Differential Equations 27 (2015), no. 3-4, 721-742.

48．Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei. Integral identity and measure estimates for stationary Fokker-Planck equations. Ann. Probab.  43(2015), no. 4, 1712-1730.

47. Huang, Wen; Ye, Xiangdong. A note on double minimality. Commun. Math. Stat. 3 (2015), no.1, 57-61.

46. Huang, Wen; Xu, Leiye; Yi, Yingfei. Asymptotic pairs, stable sets and chaos in positive entropy systems. J. Funct. Anal. 268(2015), no. 4, 824-846.

45. Feng, De-Jun; Huang, Wen; Rao, Hui. Affine embeddings and intersections of Cantor sets. J. Math. Pures Appl. (9) 102(2014), no. 6, 1062-1079.

44. Huang, Wen; Ye, Xiangdong; Zhang, Guohua. Lowering topological entropy over subsets revisited. Trans. Amer. Math. Soc.  366(2014), no. 8, 4423-4442.

43. Huang, Wen; Li, Jian; Ye, Xiangdong. Stable sets and mean Li-Yorke chaos in positive entropy systems. J. Funct. Anal.  266 (2014), no. 6, 3377–3394.

42. Huang, Wen; Shen, Weixiao. Analytic skew products of quadratic polynomials over circle expanding maps. Nonlinearity 26 (2013), no. 2, 389–404.

41. Feng, De-Jun; Huang, Wen. Variational principles for topological entropies of subsets. J. Funct. Anal.  263(2012), no. 8, 2228-254.

40. Huang, Wen; Zhang, Pengfei. Pointwise dimension, entropy and Lyapunov exponents for C1maps. Trans. Amer. Math. Soc.  364(2012), no. 12, 6355-6370.

39. Huang, Wen; Ye, Xiangdong. Generic eigenvalues, generic factors and weak disjointness.  Dynamical systems and group actions, 119-42, Contemp. Math., 567, Amer. Math. Soc., Providence, RI, 2012.

38. Huang, Wen; Li, Hanfeng; Ye, Xiangdong. Family independence for topological and measurable dynamics. Trans. Amer. Math. Soc.  364(2012), no. 10, 5209-242.

37. Chow, Shui-Nee; Huang, Wen; Li, Yao; Zhou, Haomin. Fokker-Planck equations for a free energy functional or Markov process on a graph. Arch. Ration. Mech. Anal. 203 (2012), no. 3, 969-008.

36. Li, Yao; Dwivedi, Gaurav; Huang, Wen; Kemp, Melissa L.; Yi, Yingfei. Quantification of degeneracy in biological systems for characterization of functional interactions between modules. J. Theoret. Biol.  302 (2012), 29-38.

35. Fang, Chun; Huang, Wen; Yi, Yingfei; Zhang, Pengfei. Dimensions of stable sets and scrambled sets in positive finite entropy systems. Ergodic Theory Dynam. Systems 32 (2012), no. 2, 599-628.

34. Huang, Wen; Yi, Yingfei. On Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations. Proc. Amer. Math. Soc.  140 (2012), no. 6, 1957-1962.

33. Huang, Wen; Xu, Leiye; Yi, Yingfei. Entropy of dynamical systems with repetition property. J. Dynam. Differential Equations 23(2011), no. 3, 683-693.

32. Huang, Wen; Lu, Ping; Ye, Xiangdong. Measure-theoretical sensitivity and equicontinuity. Israel J. Math. 183(2011), 233-283.

31. Huang, Wen; Ye, Xiangdong; Zhang, Guohua. Local entropy theory for a countable discrete amenable group action. J. Funct. Anal. 261(2011), no. 4, 1028-1082.

30. Chow, Shui-Nee; Huang, Wen; Li, Yao; Zhou, Haomin. A free energy based mathematical study for molecular motors. Regul. Chaotic Dyn.  16 (2011), no. 1-2, 117-127.

29. Dou, Dou; Huang, Wen; Park, Kyewon Koh. Entropy dimension of topological dynamical systems. Trans. Amer. Math. Soc.  363(2011), no. 2, 659-680.

28. Akin, E.; Glasner, E.; Huang, W.; Shao, S.; Ye, X. Sufficient conditions under which a transitive system is chaotic. Ergodic Theory Dynam. Systems 30 (2010), no. 5, 1277-1310.

27. Feng, De-Jun; Huang, Wen. Lyapunov spectrum of asymptotically sub-additive potentials. Comm. Math. Phys.  297(2010), no. 1, 1-43.

26. Huang, Wen; Ye, Xiangdong; Zhang, Guohua. Lowering topological entropy over subsets. Ergodic Theory Dynam. Systems 30 (2010), no. 1, 181-209.

25. Huang, Wen; Yi, Yingfei. Almost periodically forced circle flows. J. Funct. Anal.  257(2009), no. 3, 832-902.

24. Huang, Wen; Ye, Xiangdong. Combinatorial lemmas and applications to dynamics. Adv. Math.  220 (2009), no. 6, 1689-1716.

23. Huang, Wen. Stable sets and ϵ-stable sets in positive-entropy systems. Comm. Math. Phys.  279 (2008), no. 2, 535-557.

22. Cao, Yong-Luo; Feng, De-Jun; Huang, Wen. The thermodynamic formalism for sub-additive potentials. Discrete Contin. Dyn. Syst.  20(2008), no. 3, 639-657.

21. Blanchard, François; Huang, Wen. Entropy sets, weakly mixing sets and entropy capacity. Discrete Contin. Dyn. Syst. 20(2008), no. 2, 275-311.

20. Blanchard, François; Huang, Wen; Snoha, L'ubomír. Topological size of scrambled sets. Colloq. Math. 110 (2008), no. 2, 293-361.

19. Huang, Wen; Park, Kyewon Koh; Ye, Xiangdong. Topological disjointness from entropy zero systems. Bull. Soc. Math. France 135 (2007), no. 2, 259-282.

18. Huang, Wen; Yi, Yingfei. A local variational principle of pressure and its applications to equilibrium states. Israel J. Math. 161 (2007), 29-74.

17. Huang, Wen; Ye, Xiangdong; Zhang, Guohua. Relative entropy tuples, relative U.P.E. and C.P.E. extensions. Israel J. Math. 158 (2007), 249-283.

16. Huang, Wen. Tame systems and scrambled pairs under an abelian group action. Ergodic Theory Dynam. Systems 26 (2006), no. 5, 1549-1567.

15. Dou, Dou; Huang, Wen; Ye, Xiangdong. Null flows and null functions on R. J. Dynam. Differential Equations 18 (2006), no. 1, 197-221.

14. Huang, Wen; Ye, Xiangdong. A local variational relation and applications. Israel J. Math.  151 (2006), 237-279.

13. Huang, Wen; Ye, Xiangdong; Zhang, Guohua. A local variational principle for conditional entropy. Ergodic Theory Dynam. Systems 26 (2006), no. 1, 219-245.

12. Huang, Wen; Shao, Song; Ye, Xiangdong. Mixing via sequence entropy.  Algebraic and topological dynamics, 101-122, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, 2005

11. Huang, Wen; Ye, Xiangdong. Dynamical systems disjoint from any minimal system. Trans. Amer. Math. Soc.  357(2005), no. 2, 669-694.

10. Huang, Wen; Maass, Alejandro; Ye, Xiangdong. Sequence entropy pairs and complexity pairs for a measure. Ann. Inst. Fourier (Grenoble) 54 (2004), no. 4, 1005-1028.

9. Huang, W.; Maass, A.; Romagnoli, P. P.; Ye, X. Entropy pairs and a local Abramov formula for a measure theoretical entropy of open covers. Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1127-1153.

8. Huang, Wen; Ye, Xiangdong. Minimal sets in almost equicontinuous systems. Tr. Mat. Inst. Steklova 244 (2004), Din. Sist. i Smezhnye Vopr. Geom., 297–304; reprinted in Proc. Steklov Inst. Math.  2004, no. 1(244), 280-287.

7. Huang, Wen; Shao, Song; Ye, Xiangdong. Mixing and proximal cells along sequences. Nonlinearity 17 (2004), no. 4, 1245-1260.

6. Huang, Wen; Ye, Xiangdong. Topological complexity, return times and weak disjointness. Ergodic Theory Dynam. Systems 24 (2004), no. 3, 825-846

5. Huang, Wen; Li, Simin; Shao, Song; Ye, Xiangdong. Null systems and sequence entropy pairs. Ergodic Theory Dynam. Systems 23 (2003), no. 5, 1505–1523.

4. Huang, Wen; Ye, Xiangdong. An explicit scattering, non-weakly mixing example and weak disjointness. Nonlinearity 15 (2002), no. 3, 849-862.

3. Huang, Wen; Ye, Xiangdong. Devaney's chaos or 2-scattering implies Li-Yorke's chaos. Topology Appl.  117 (2002), no. 3, 259-272.

2. Huang, Wen; Ye, Xiangdong. Non-wandering sets of the powers of maps of a tree. Sci. China Ser. A 44 (2001), no. 1, 31-39.

1. Huang, Wen; Ye, Xiangdong. Homeomorphisms with the whole compacta being scrambled sets. Ergodic Theory Dynam. Systems 21 (2001), no. 1, 77-91.

 

3.专著(Monographs)

 1. 叶向东、黄文、邵松，拓扑动力系统概论，科学出版社，2008.

(Ye Xiangdong, Huang Wen, Shao Song, An Introduction to Topological Dynamical Systems, Science Press, 2008.)

 2. 叶向东、黄文、邵松，遍历理论及其应用，待出版

(Ye Xiangdong, Huang Wen, Shao Song, Ergodic Theory and Its Applications, forthcoming.)