Welcome to Jianyu Chen's Homepage

      Jianyu Chen
      Visiting Assistant Professor
      Department of Mathematics and Statistics
      Lederle Graduate Research Tower 1030
      University of Massachusetts Amherst
      710 N. Pleasant Street, Amherst, MA 01003
      Email: jchen@math.umass.edu
      Phone: 413-545-7702

Education

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).

Employment

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 - present. (Supervisor: Professor Hongkun Zhang )

Research Interests

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.

Publications and Preprints

Publications:

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.

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 toral extensions over certain hyperbolic skew products , preprint.

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

4. (With Fang Wang and Hong-Kun Zhang) Markov Partitions and Thermodynamic Formalism for Hyperbolic Systems with Singularities, submitted.

5. (With Hong-Kun Zhang) Coupling Lemma and Stochastic Properties for One-dimensional Expanding Maps, preprint.

6. (With Huyi Hu, Yakov Pesin and Ke Zhang) The Essential Coexistence Phenomenon in Hamiltonian Systems, preprint.

7. (With Hong-Kun Zhang) Statistical properties of one-dimensional expanding maps with singularities of low regularity (pdf), submitted.

Teaching Experiences

I am currently teaching STAT 515 - Statistics I, Spring 2019, at Umass Amherst. Please find information on the course webpage .

Here is my full teaching list.

Some Useful Links

American Mathematical Society, MathSciNet
The Center for Dynamics and Geometry at Pennstate
Encyclopedia of dynamical systems
dynamical-systems.org