I completed my Ph.D. study at Brigham Young University, advised by Kening Lu. I am currently a postdoc in the math department at University of Arizona, mentored by Qiudong Wang. Here is my CV.

I am interested in understanding chaotic behavior of dynamical systems, especially systems from physical models given by (stochastic) differential equations, for example, the Navier-Stokes equations from fluid mechanics, the N-body problem from celestial mechanics, and dynamical systems on graphs.

**Publications and Preprints: **

**Publications and Preprints:**

Liu, R., Lu, K.: Ergodicity and mixing of quasi-periodically forced 2D stochastic Navier-Stokes Equations and limit theorems in the hypoelliptic setting. arXiv preprint arXiv:2205.14348. 1-54. Submitted. (2022)

Liu, R., Lu, K.: Statistical Properties of 2D Stochastic Navier-Stokes Equations with Time-Periodic Forcing and Degenerate Stochastic Forcing. arXiv preprint arXiv:2105.00598. 1-68. Submitted. (2021)

Liu, R., Yan, D.: Exclusion of quadruple collisions in minimizers of the planar equal-mass N-body problem. J. Differential Equations. 287, 113–147 (2021)

Liu, R., Li, J., Yan, D.: New periodic orbits in the planar equal-mass three-body problem. Discrete Contin. Dyn. Syst. 38(4), 2187–2206 (2018)

Shi, B., Liu, R., Yan, D., Ouyang, T.: Multiple periodic orbits connecting a collinear configuration and a double isosceles configuration in the planar equal-mass four-body problem. Adv. Nonlinear Stud. 17(4), 819–835 (2017)

Yan, D.,Liu, R., Hu, X., Mao, W., Ouyang, T.: New phenomena in the spatial isosceles three-body problem with unequal masses. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 25(12), 1550169 (2015)

Yan, D., Liu, R., Chang, G.: A type of multiple integral with log-gamma function. Involve. 8(4), 593–614 (2015)

**Teaching:**

**Teaching:**

*University of Arizona, Instructor:*

Fall 2022: MATH 125 - Calculus I

*Brigham Young University, Instructor:*

Spring 2021: MATH 116 - Essentials of Calculus

Summer 2020: MATH 113 - Calculus II

*Brigham Young University, Teaching Assistant:*

Fall - Winter 2021: MATH 341 - Theory of Analysis I

Fall - Winter 2020 : MATH 341 - Theory of Analysis I

Fall 2019: MATH 112 - Calculus I