姚潇

复动力系统以及分形几何与复分析相关交叉领域

如果对复分析、复动力系统有兴趣的同学，可以尝试阅读部分材料

1.Shen和Rempe的科普性论文[1408.1129] The exponential map is chaotic: An invitation to transcendental dynamics

2.Misiurewicz的短文On iterates of ez | Ergodic Theory and Dynamical Systems | Cambridge Core

3.Ahlfors的复分析

4 Rudin的实分析与复分析

5:Beals和Wong的两本书Explorations in complex functions, More explorations in complex functions

6:Devaney的指数函数动力系统综述augsburg.pdf.

7:Fornaess的简短的讲义[1605.09562] Introduction to complex dynamics in one dimension

8:Bergweiler的讲义 37.pdf

9: Rempe和Bergweiler的综述[2507.11370] The escaping set in transcendental dynamics

10: Milnor著名的讲义 Dynamics in one complex variable

数学分析3-1,数学分析3-2 (本科生习题课)

2021秋季学期   数学分析3-3 （强基班）

2022春季学期   现代分析基础（实分析与复分析） （本科生，研究生合上）

2022秋季学期   数学分析3-3 （省身班）

2023春季学期   实分析与复分析（研究生）

2023秋季学期   数学分析3-3 （省身班）

2024春季学期    实分析与复分析（研究生）

2024年秋季学期   数学分析3-3 （省身班）

2025年春季学期   实分析与复分析（研究生）

2025年秋季学期   数学分析3-3（省身班）

3.复方法在非局部算子、函数代数独立性、薛定谔算子和差分唯一性的应用.43.5万元，2024-01-01至2027-12-31.

2. 国家自然科学基金青年基金项目(主持), Julia集上的Lyapunov指数和Birkhoff谱及复方法在薛定谔算子的应用, 21万元，2020-01-01至2022-12-31.

1.教育部高校基本科研业务费（主持), 14.5万元，2019.01.-2020.12.

23. The difference analogue of the Tumura-Hayman-Clunie theorem. Bulletin of the Australian Mathematical Society. 2023:1-10. doi:10.1017/S0004972723001089. (with H. Li, M. L. Fang)

22. Uniqueness on Difference Operators of Meromorphic Functions of Infinite Order. Acta. Math. Sin.-English Ser. (2023). https://doi.org/10.1007/s10114-023-2300-x. (with H. Li, M. L. Fang)

21. Inequalities Concerning Maximum Modulus and Zeros of Random Entire Functions. Proceedings of the Edinburgh Mathematical Society. 2023:1-22. doi:10.1017/S0013091523000639. (with H. Li, J. Wang, Z. Ye)

20. A Difference Version of the Rubel-Yang–Mues-Steinmetz–Gundersen Theorem. Comput. Methods Funct. Theory (2023). (with M.L. Fang, H. Li, W.Q.Shen)

19. Difference independence of the Euler gamma function. Chinese Ann. Math. Ser. B 44 (2023), no. 4, 481–488.(with Q.Y. Wang)

18. The spectrum of periodi-doubling Hamiltonian. Commun. Math. Phys.   2（2022).  (with

Q. H. Liu, Y. H. Qu).

17. Rationality of meromorphic functions between real algebraic sets in the plane. Proc. AMS (2022), (Accept). (with T.W. Ng). 

16. Multifractal analysis in non-uniformly hyperbolic interval maps. Nonlinearity 35 (2022), no. 1, 110–133. (with G. Z. Ma, W. Q. Shen)

15. Julia Limiting Directions of Entire Solutions of Complex Differential Equations. Acta Math. Sci. Ser. B (Engl. Ed.) 41 (2021), no. 4, 1275–1286. (with J. Wang, C. C. Zhang)

14. A relation between moments of Liu process and Bernoulli numbers. Fuzzy Optim. Decis. Mak. 20 (2021), no. 2, 261–272. （with G. Z. Ma, X. F. Yang）

13. On Julia limiting directions of meromorphic functions. Israel J. Math. 238 (2020), no. 1, 405–430.

(with J. Wang)

12. Fractional Sobolev spaces from a complex analytic viewpoint. J. Funct. Anal. 279 (2020), no. 7, 108651, 27 pp. (with Z.Q. Zhang)

11. Characterizations of all real solutions for the KdV equation and WR. Appl. Math. Lett. 107 (2020), 106446, 8 pp. (with Y.Y. Gu, C. F. Wu, W. J. Yuan)

10.Singular direction and q-difference operator of meromorphic functions. Bull. Malays. Math. Sci. Soc. 43 (2020), no. 5, 3693–3709. (with J. R. Long, J. Y. Qiao) 

9.Function theory on annuli. Complex Var. Elliptic Equ. 64 (2019), no. 7, 1103–1124.

(with F.J. Chai, D.C. Sun, W.Q. Shen)

8. Lyapunov exponents and related concepts for entire functions. Math. Z. 288 (2018), no. 3-4, 855–873. (with W. Bergweiler, J.H. Zheng)

7. Analytic properties for holomorphic matrix-valued maps in C^{2×2}. Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 11, 1536–1548. (with C.Fu, Y.Z. Li)

6. Hausdorff dimension of the irregular set in non-uniformly hyperbolic systems. Fractals 25 (2017), no. 3, 1750027, 10 pp. (with G.Z. Ma)

5.  Multifractal analysis of the historic set in non-uniformly hyperbolic systems. Arch. Math. (Basel) 108 (2017), no. 4, 405–413. (with G.Z. Ma)

4. Unbounded trace orbits of Thue-Morse Hamiltonian. J. Stat. Phys. 166 (2017), no. 6, 1509–1557.(with Q.H. Liu, Y. H. Qu)

3. Multifractal analysis of dimension spectrum in non-uniformly hyperbolic systems. Mediterr. J. Math. 13 (2016), no. 5, 3069–3090. (with G.Z. Ma)

2. Higher dimensional multifractal analysis of non-uniformly hyperbolic systems. J. Math. Anal. Appl. 421 (2015), no. 1, 669–684. (with G.Z. Ma)

1. Poincáre recurrence theorem in regular uncertain dynamic system. Fuzzy Optim. Decis. Mak. 13 (2014), no. 3, 319–328. (with H. Ke)