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: ProfessorYakov Pesin).

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

Visiting Assistant Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst, 2016 - 2019. (Supervisor: ProfessorHongkun 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. (WithYakov 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. (WithHuyi HuandYakov 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. (WithHuyi HuandYakov 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. (WithYun YangandHong-Kun Zhang) Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities (pdf), J. Stat. Phys. 172 (2018), no. 6, 1499-1524.

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

8. (WithHong-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. (WithHuyi Huand Yunhua Zhou) SRB measures for pointwise hyperbolic systems on open regions (pdf), Sci.China Math. 63 (2020), no. 9, 1671–1720.

10. (WithHuyi HuandYakov PesinandKe Zhang) The essential coexistence phenomenon in Hamiltonian dynamics (pdf), Ergodic Theory Dynam. Systems 42 (2022), no. 2, 592–613.