Most Current Research Interests of Yunping Jiang

·       Number Theory and Ergodic Theory

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

2.      Oscillating sequences, MMA and MMLS flows and Sarnak’s conjecture (with Aihua Fan). Ergod. Th. & Dynam. Sys., August 2018, Vol. 38, no. 5, 1709–1744. https://doi.org/10.1017/etds.2016.121

3.      Higher order oscillation and uniform distribution (with Shigeki Akiyama). Uniform Distribution Theory, Volume 14 (2019), no. 1, 1-10. https://doi.org/10.2478/udt-2019-0001

4.      Orders of oscillation motivated by Sarnak's conjecture. Proceedings of AMS, Volume 147, Number 7, July 2019, 3075-3085. https://doi.org/10.1090/proc/14487

·       Complex Dynamics

1.      Cycle doubling, merging and renormalization in the tangent family (with Tao Chen and Linda Keen). Conformal Geometry and Dynamics, AMS, Volume 22 (2018), 271–314. https://doi.org/10.1090/ecgd/327

2.      Slices of parameter space for meromorphic maps with two asymptotic values (with Tao Chen and Linda Keen). Ergodic Theory and Dynamical Systems First View , pp. 1 – 41, DOI: https://doi.org/10.1017/etds.2021.108. aXiv Preprint https://arxiv.org/pdf/1908.06028.pdf

3.     Accessible Boundary Points in the Shift Locus of a Family of Meromorphic Functions with Two Finite Asymptotic Values (with Tao Chen and Linda Keen). Arnold Mathematical Journal. Online First, January 7, 2021. https://doi.org/10.1007/s40598-020-00169-1

4.      A framework towards understanding the characterization of holomorphic maps (an Appendix on Transcendental Functions by Tao Chen, Yunping Jiang, and Linda Keen). Frontiers in Complex Dynamics, March 2014, Princeton University Press, 235-253. http://www.jstor.org/stable/j.ctt5vjv7b.15

·       Metric Entropy in Smooth Dynamical Systems

1.      Global graph of metric entropy on expanding Blaschke products. Discrete and Continuous Dynamical Systems, Online First, September 2020. http://dx.doi.org/10.3934/dcds.2020325

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. http://dx.doi.org/10.3934/dcds.2017205

3.      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. http://dx.doi.org/10.3934/dcds.2008.22.215

4.      Distance entropy of dynamical systems on noncompact phase spaces (with Xiongping Dai). Discrete and Continuous Dynamical Systems, Vol. 20, No. 2 (2008), 313-333. http://dx.doi.org/10.3934/dcds.2008.20.313

·        Applications of Quasiconformal Mappings and Teichmüller Theory to Dynamical Systems and vice versa

1.      Geometric Gibbs theory. Science China Mathematics, September 2020, Vol. 63, no. 9, 1777-1824.  https://doi.org/10.1007/s11425-019-1638-6

2.      Symmetric rigidity for circle endomorphisms with bounded geometry (with John Adamski, Yunchun Hu, Yunping Jiang, and Zhe Wang). The Proceedings of the American Mathematical Society, 150 (2022), 3581-3593. https://www.ams.org/journals/proc/2022-150-08/S0002-9939-2022-15921-8/home.html.  https://arxiv.org/pdf/2101.06870.pdf

3.      Symmetric invariant measures.  Contemporary Mathematics, AMS, Vol. 575, 2012, 211-218. http://dx.doi.org/10.1090/conm/575/11399

4.      A function model for the Teichmüller space of a closed hyperbolic Riemann surface. Science China Mathematics, November 2019, Vol. 62, No. 11, 2249-2270. https://doi.org/10.1007/s11425-019-9520-4

·       Holomorphic Motions

1.      Holomorphic motions and related topics (with Frederick Gardiner and Zhe Wang). Geometry of Riemann SurfacesLondon Mathematical Society Lecture Note Series, No. 368, 2010, 156-193.

2.      Winding numbers and full extendibility in holomorphic motions. Conformal Geometry and Dynamics, AMS, May 26, 2020, Vol. 24, 109-117. https://doi.org/10.1090/ecgd/351

3.      Monodromy, liftings of holomorphic maps, and extensions of holomorphic motions (with Sudeb Mitra). Conformal Geometry and Dynamics, Volume 22 (2018), 333–344. https://doi.org/10.1090/ecgd/329

4.      Teichmüller spaces and tame quasiconformal motions (with Sudeb Mitra, Hiroshige Shiga, and Zhe Wang). Tohoku Mathematical Journal, The Second Series, Vol. 70 (2018), No. 4, 607-631.

·       Transfer Operators and Thermodynamical Formalism

1.     Nanjing Lecture Notes in Dynamical Systems. Part One: Transfer Operators in Thermodynamical Formalism. FIM Preprint Series, ETH-Zurich, June 2000.

2.     Convergence speed of a Ruelle operator associated with a non-uniformly expanding conformal dynamical system and a Dini potential. Discrete and Continuous Dynamical Systems (with Yuan-Ling Ye). Discrete and Continuous Dynamical Systems., Volume 38, Number 9 (2018), 4693-4713. http://dx.doi.org/10.3934/dcds.2018206

3.     Ruelle operator theorem for nonexpansive systems (with Yuan-Ling Ye). Ergodic Theory and Dynamical Systems, (2010), 30, 469–487. https://doi.org/10.1017/S014338570900025X

4.     Decay of correlations for weakly expanding dynamical systems with Dini potentials under optimal quasi-gap condition (with Yuan-Ling Ye). NonlinearityVolume 35 (2022)Number 2, 916-953. https://doi.org/10.1088/1361-6544/ac3c2c