Name：Jianyu Chen

B.S., Mathematics and Yuanpei Program, Peking University , Beijing, China, 2003-2007.

Ph.D., Mathematics, The Pennsylvania State University, 2007-2012. (Advisor: Professor Yakov Pesin).

Visiting Assistant Professor, Department of Mathematics, Michigan State University, 2012-2016. (Supervisor: Professor Huyi Hu)

Visiting Assistant Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst, 2016 - 2019. (Supervisor: Professor Hongkun Zhang )

My research interests lie in dynamical systems and ergodic theory, more specifically, in the following aspects:

(1) The coexistence phenomenon of chaotic behavior and regular behavior in smooth systems;

(2) The existence and uniqueness of SRB measures for some nonuniformly partially hyperbolic systems;

(3) Stochastic properties of some hyperbolic systems, such as decay of correlations, central limit theorem, etc.;

(4) Fractal geometry and dimension theory in dynamical systems;

(5) The applications of the above theories in billiard dynamics and other physical models.

1. (With Yakov Pesin) Dimension of non-conformal repellers: a survey (pdf1, pdf2), Nonlinearity 23 (2010), no. 4, R93-R114.

2. On essential coexistence of zero and nonzero Lyapunov exponents (pdf1, pdf2), Discrete Contin. Dyn. Syst. 32 (2012), no. 12, 4149-4170.

3. (With Huyi Hu and Yakov Pesin) A volume preserving flow with essential coexistence of zero and nonzero Lyapunov exponents (pdf1, pdf2), Ergodic Theory Dynam. Systems 33 (2013), no. 6, 1748-1785.

4. (With Huyi Hu and Yakov Pesin) The essential coexistence phenomenon in dynamics (pdf1, pdf2), in special issue Statistical Properties of Dynamical Systems'', Dynamical Systems, an International Journal, v. 28, 2013.

5. (With Yun Yang and Hong-Kun Zhang) Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities (pdf), J. Stat. Phys. 172 (2018), no. 6, 1499-1524.

6. (With Kien Nguyen) Invariance Principles for Ergodic Systems with Slowly α-mixing Inducing Base (pdf), USUZCAMP 2017. Differential Equations and Dynamical Systems, 115--126. Springer Proceedings in Mathematics & Statistics, vol 268. Springer, Cham..

7. (With Huyi Hu) The Spectral Gap for Transfer Operators of Torus Extensions over Expanding Maps (pdf), Nonlinearity 32 (2019), no. 1, 356–393.

8. (With Hong-Kun Zhang) Statistical properties of one-dimensional expanding maps with singularities of low regularity (pdf), Discrete Contin. Dyn. Syst. 39 (2019), no. 9, 4955-4977.

9. (With Huyi Hu and Yunhua Zhou) SRB measures for pointwise hyperbolic systems on open regions (pdf), Sci.China Math. 63 (2020), no. 9, 1671–1720.

10. (With Huyi Hu and Yakov Pesin and Ke Zhang) The essential coexistence phenomenon in Hamiltonian dynamics (pdf), Ergodic Theory Dynam. Systems 42 (2022), no. 2, 592–613.