Jianyu Chen

Visiting Assistant Professor

C236 Wells Hall

Department of Mathematics

Michigan State University

East Lansing, MI 48824

Email: jychen@math.msu.edu

Phone: (517) 353-2928

I was born in Fuzhou, China, and got my B.S. in Mathematics at Peking University , Beijing, China in 2007. In 2012, I accomplished my Ph.D. degree in Mathematics at the Pennsylvania State University under the supervision of Professor Yakov Pesin. Right now I am a visiting Assistant Professor in the department of Mathematics at Michigan State University, working with Prof. Huyi Hu.

My research interests lie in dynamical systems and ergodic theory. Currently, I am working on the theory of nonuniform and partial hyperbolicity in smooth dynamical systems, more specifically, in the following aspects:

(a) the "coexistence phenomenon" of zero and nonzero Lyapunov exponents in various smooth systems;

(b) Existence of SRB measures for some nonuniformly or partially hyperbolic systems;

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

I am also interested in fractal geometry and dimension theory in dynamical systems.

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.

Preprints:

1. (With Huyi Hu and Yunhua Zhou) The existence of SRB measures for some hyperbolic systems on an open region, Preprint.2. (With Huyi Hu) Exponential mixing of torus extensions over expanding maps , Submitted to Trans. Amer. Math. Soc.

3. (With Huyi Hu) Exponential mixing of toral extensions over certain hyperbolic skew products , preprint.

4. Statistical properties of Lie group extensions over expanding Young towers , preprint.

Here is my full teaching list.

American Mathematical Society,
MathSciNet

The Center for Dynamics and Geometry at Pennstate

Encyclopedia of dynamical systems

dynamical-systems.org