These are my most current research interests:

· **Number Theory and Ergodic Theory**

1. Zero entropy continuous interval
maps and MMLS-MMA property. Nonlinearity 31 (2018) 2689–2702.
doi:10.1088/1361-6544/aab593

2. Oscillating
sequences, MMA and MMLS flows and Sarnak's conjecture
(with Aihua Fan). Erg. Th. & Dyn.
Sys., Published Online March 14, 2017. doi:10.1017/etds.2016.121

3. Higher order oscillation and uniform
distribution (with Shigeki
Akiyama).** **Uniform
Distribution Theory. To appear.

4. Higher
order oscillating sequences, affine distal flows on the d-torus, and Sarnak's conjecture. arXiv1612.04306v2

· **Complex Dynamics**

1.
A framework towards
understanding the characterization of holomorphic maps
(with an Appendix on transcendental functions written with Tao Chen
and Linda Keen). Frontiers
in Complex Dynamics, March 2014, Princeton University Press, 235-253.

2.
Bounded geometry and characterization of some transcendental
maps (with Tao Chen and Linda Keen). Indiana University
Mathematics Journal, Math. J. **66** (2017),
1537-1571.

3.
Cycle doubling, merging and
renormalization in the tangent family (with Tao Chen and Linda Keen). arXiv:1708.01808v1.

4.
Geometrization of
sub-hyperbolic semi-rational branched coverings (with Tao Cheng). arXiv1207.1292.

· **Quasiconformal**** Mappings and Teichmüller Spaces **

1.
Teichmüller spaces and tame quasiconformal motions (with Sudeb
Mitra, Hiroshige Shiga, and Zhe
Wang). Tohoku Mathematical Journal, accepted 2016 and to
appear on Vol. 71, no. 1, March 2019.

2.
Monodromy,
liftings of holomorphic maps, and extensions of holomorphic motions (with Sudeb Mitra). arXiv1804.03773v1

3.
An
explicit counter-example to the full extendibility problem in holomorphic
motions. arXiv:1804.04067v1

· **Metric Entropy in
Smooth Dynamical Systems**

1.
Infimum of the metric
entropy of hyperbolic attractors with respect to the SRB measure (with
Huyi Hu and Miaohua Jiang). Discrete and Continuous Dynamical Systems,
Vol. 22, No. 1&2
(2008), 215–234.

2.
Infimum of the
metric entropy of volume preserving Anosov systems (with Huyi Hu and Miaohua Jiang).
Discrete and Continuous Dynamical Systems, Volume 37 (2017), No. 9, 4767-4783.

3.
Infimum of metrtic entropy and the Boole map. Preprint.

· **Transfer Operators and
Gibbs Measures**

1. Convergence speed of a Ruelle operator associated with a non-uniformly expanding
conformal dynamical system and a Dini potential. Discrete and Continuous Dynamical Systems. To
appear, 2018.

· **Applications of Quasiconformal Mappings and Teichmüller
Theory to Dynamical Systems**

1.
An introduction to geometric
Gibbs theory. Dynamics, Games and Science, CIM Series in
Mathematical Sciences, Vol. 1, Springer-Verlag, 2015, 327-339.

2.
Symmetric invariant measures. Contemporary Mathematics, AMS, Vol. 575, 2012, 211-218.

3.
Simultaneous uniformization for
uniformly quasisymmetric circle dynamical
systems (with Fred Gardiner). Dynamical Systems,
Vol. 30 (2015), No. 4, 543–565.

4.
Teichmueller structures
and dual geometric Gibbs type measure theory for continuous potentials. arXiv:0804.3104v3

5.
Bers complex manifold structure
on circle diffeomorphisms. Submitted Preprint.

· **Applications of
Dynamical Systems to Teichmüller Theory**

**1.
** Function model of
the Teichmueller space of a closed hyperbolic Riemann surface. arXiv:0810.4969v3

If you are interested in a complete list of my publications
and my co-authors, please go to the list of
publications.