List of Publications

Yunping Jiang

 

Journal Articles

   2020-Present

1.     Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms. Acta Mathematica Sinica, English Series, March 2020, Vol. 36, no. 3, 245-272. https://doi.org/10.1007/s10114-020-7502-x

2.     Volume of the Hyperbolic Cantor sets (with Habibulla Akhadkulov). Dynamical Systems, 2020, Vol. 35, no. 2, 185-196. https://doi.org/10.1080/14689367.2019.1659754

3.     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

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

5.     Global graph of metric entropy on expanding Blaschke products. Discrete and Continuous Dynamical Systems, Volume 41, Number 3, March 2021, 1469-1482. http://dx.doi.org/10.3934/dcds.2020325

6.     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

7.     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 https://arxiv.org/pdf/1908.06028.pdf

8.     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

9.     Symmetric rigidity for circle endomorphisms with bounded geometry (with John Adamski, Yunchun Hu, Yunping Jiang, and Zhe Wang). To appear in the Proceedings of the American Mathematical Society. https://arxiv.org/pdf/2101.06870.pdf

   2015-2019

1.     Angle geometry in universal Teichmüller space (with Jinhua Fan). Proceedings of American Mathematical Society, 143 (2015) 1651-1659. https://doi.org/10.1090/S0002-9939-2014-12352-5

2.     Guiding isotopies and holomorphic motions (with Fred Gardiner and Zhe Wang). Annales Academiæ Scientiarum Fennicæ Mathematica, Volumen 40, 2015, 485–501. http://www.acadsci.fi/mathematica/Vol40/vol40pp485-501.pdf

3.     An introduction to geometric Gibbs theory. A Chapter in Dynamics, Games and Science (edited by J.-P. Bourguignon, Jelstch, A. Pinto, and M. Viana), Springer-Verlag, 2015, 327-339. https://doi.org/10.1007/978-3-319-16118-1_18

4.     Foreword for Dynamics, Games and Science (edited by J.-P. Bourguignon, Jelstch, A. Pinto, and M. Viana), Springer-Verlag, 2015, v-vi. https://doi.org/10.1007/978-3-319-16118-1

5.      Complex Dynamics and Entropy. 2013 Institutional Lecture Notes, Science Publication, 2015, 76-85.

6.     Simultaneous uniformization for uniformly quasisymmetric circle dynamical systems (with Fred Gardiner). Dynamical Systems: An International Journal, Vol. 30, Issue 4, 2015, 543-565. http://dx.doi.org/10.1080/14689367.2015.1082537

7.     Bounded geometry and families of meromorphic functions with two asymptotic values (with Tao Chen and Linda Keen). Proceedings of the Six International Congress of Chinese Mathematicians, Higher Education Press and International Press, Beijing-Boston, ALM37 (2016), 355-373.

8.     Variation of moduli under continuous motions (with Sudeb Mitra). The Proceedings of the 6th Ahlfors-Bers Colloquium. Contemporary Mathematics, AMS, Vol. 696 (2017), 205-214. http://dx.doi.org/10.1090/conm/696/14023

9.     Bounded geometry and characterization of some transcendental maps (with Tao Chen and Linda Keen). Indiana University Mathematics Journal, 66 (2017), 1537-1571. http://dx.doi.org/10.1512/iumj.2017.66.5990

10.  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

11.  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

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

13.  Oscillating sequences, MMA and MMLS flows and Sarnak’s conjecture (with Aihua Fan). 

Ergodic Theory & Dynamical. Systems, August 2018, Vol. 38, no. 5, 1709–1744. https://doi.org/10.1017/etds.2016.121

14.  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

15.  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. https://projecteuclid.org/euclid.tmj/1546570827

16.  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

17.  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

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

19.  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

   2010-2014

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

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

22.  Function models for Teichmuller spaces and dual geometric Gibbs type measure theory for circle dynamics. Teichmueller Theory and Moduli Problem, RMS LECTURE NOTES SERIES, No.10, 2010, 413-435.

23.  Asymptotically affine and asymptotically conformal circle endomorphisms (with Frederick Gardiner). RIMS Kôkyûroku Bessatsu B17, Infinite Dimensional Teichmuller Spaces and Moduli Spaces, Ed. Ege Fujikawa, June 2010, 37-53.

24.  Quasisymmetric property for conjugacies between Anosov diffeomorphisms of the two-torus (with Huyi Hu). Science China in Mathematics, Vol. 53 (2010), No. 3: 663–670. https://doi.org/10.1007/s11425-010-0061-3

25.  Geometrically finite and semi-rational branched coverings of the two-sphere (with Guizhen Cui). Transactions of the American Mathematical Society, Vol. 363, Number 5, May 2011, 2701-2714. https://doi.org/10.1090/S0002-9947-2010-05211-0

26.  Differential rigidity and applications in one-dimensional dynamics. Dynamic Games and Science I, Springer Proceedings in Mathematics, 2011, 487-502. https://doi.org/10.1007/978-3-642-11456-4_31

27.  Kobayashi's and Teichmuller's metrics on the Teichmuller space of symmetric circle homeomorphisms (with Jun Hu and Zhe Wang). Acta Mathematica Sinica, English Series, March 2011, Vol. 27, No. 3, pp. 617–624. https://doi.org/10.1007/s10114-011-9045-7

28.  Extending holomorphic motions and monodromy (with Michael Beck, Sudeb Mitra, and Hiroshige Shiga). Annales Academiæ Scientiarum Fennicæ Mathematica, Vol. 37 (2012), 53-67. http://dx.doi.org/10.5186/aasfm.2012.3713

29.  Quasiconformal motions and isomorphisms of continuous families of Mobius groups (with Sudeb Mitra and Hiroshige Shiga). Israel Journal of Mathematics, 188 (2012), 177–194. https://doi.org/10.1007/s11856-011-0098-1

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

31.  Douady-Earle section, holomorphic motions, and some applications (with Sudeb Mitra). Contemporary Mathematics, AMS, Vol. 575, 2012, 219-252. http://dx.doi.org/10.1090/conm/575/11399

32.  Normal families and holomorphic motions over infinite dimensional parameter spaces (with Michael Beck and Sudeb Mitra). Contemporary Mathematics, AMS, Vol. 573, 2012, 1-10. http://dx.doi.org/10.1090/conm/573/11409

33.  Circle endomorphisms, dual circles and Thompson’s group (with Frederick P. Gardiner). Contemporary Mathematics, AMS, Vol. 573, 2012, 99-118. http://dx.doi.org/10.1090/conm/573/11396

34.  A gluing theorem for quasiconformal mappings (with Yi Qi). Kodai Mathematical Journal, 35 (2012), 415–424. https://projecteuclid.org/euclid.kmj/1352985446

35.  No invariant line fields on escaping sets of the sine family (with Tao Chen and Gaofei Zhang). Discrete and Continuous Dynamical Systems. Volume 33, Number 5, May 2013. http://dx.doi.org/10.3934/dcds.2013.33.1883

36.  Martingales for quasisymmetric systems and complex manifold structures (with Yunchun Hu and Zhe Wang). Annales Academiæ Scientiarum Fennicæ Mathematica, Volumen 38, 2013, 1–26. http://dx.doi.org/10.5186/aasfm.2013.3812

37.  Conformally natural extensions in view of dynamics (with Sudeb Mitra and Zhe Wang). Kodai Mathematical Journal, Kodai Math. J., 36 (2013), 167–173. http://dx.doi.org/10.2996/kmj/1364562727

38.  Canonical Thurston obstructions for sub-hyperbolic semi-rational branched coverings (with Tao Chen).  Conformal Geometry and Dynamics, Volume 17 (2013), 6–25. https://doi.org/10.1090/S1088-4173-2013-00250-6

39.  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

   2004-2009

  1. Scaling functions for degree two circle endomorphisms (with Guizhen Cui and Frederick Gardiner). Contemporary Mathematics, AMS Series, Vol. 355 (2004), 147-163. http://dx.doi.org/10.1090/conm/355/06450
  2. Local connectivity of the Mandelbrot set at certain infinitely renormalizable points. Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 236-264. https://www.intlpress.com/site/pub/pages/books/items/00000019/index.php
  3. On geometrically finite branched covering maps-I. Locally combinatorial attracting (with Guizhen Cui and Dennis Sullivan). Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 1-14. https://www.intlpress.com/site/pub/pages/books/items/00000019/index.php
  4. On geometrically finite branched covering maps-II. Realization of rational maps (with Guizhen Cui and Dennis Sullivan). Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 15-29. https://www.intlpress.com/site/pub/pages/books/items/00000019/index.php
  5. On geometrically finite branched covering maps-III. A direct proof of CJS Theorem (with Gaofei Zhang).  Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 265-291. https://www.intlpress.com/site/pub/pages/books/items/00000019/index.php
  6. Spectral theory of transfer operators (with Aihua Fan). Complex Dynamics and Related Topics, New Studies in Advanced Mathematics, 2004, The International Press, 63-128. https://www.intlpress.com/site/pub/pages/books/items/00000019/index.php
  7. On conformal measures for infinitely renormalizable quadratic polynomials (with Zhiyong Huang and Yuefei Wang). Science in China, Ser. A Mathematics, Vol. 48 (2005), no. 10, 1411-1420.  (Chinese Version: 35(9) (2005)). https://doi.org/10.1360/04ys0221
  8. Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy (with Xiongping Dai). Journal of Statistical Physics, Vol. 120, NOS 3/4, August 2005, 511-519. https://doi.org/10.1007/s10955-005-7008-z
  9. Asymptotic Hausdorff dimensions of Cantor sets associated with an asymptotically non-hyperbolic family (with Aihua Fan and Jun Wu). Ergod. Th. & Dynam. Sys., 25 (2005), no. 6, 1799-1808. https://doi.org/10.1017/S014338570500009X
  10. Metric invariants in dynamical systems. Journal of Dynamics and Differential Equations, Vol. 17 (2005), no. 1, 51 – 71. https://doi.org/10.1007/s10884-005-5403-4
  11. Differentiable rigidity and smooth conjugacy. Annales Academiæ Scientiarum Fennicæ Mathematica, Vol. 30 (2005), 361-383. https://www.acadsci.fi/mathematica/Vol30/jiang.pdf
  12. Analyticity of the susceptibility function for unimodal Markovian maps of the interval (with David Ruelle). Nonlinearity, 18 (2005), 2447-2453. 10.1088/0951-7715/18/6/002
  13. Asymptotically conformal fixed points and holomorphic motions. Complex Analysis and Applications, Proceedings of the 13th international conference on finite or infinite dimensional complex analysis and applications, 2006, 109-129. (This the preprint version of 68.) https://doi.org/10.1142/9789812773159_0010
  14. Some applications of universal holomorphic motions (with Sudeb Mitra). Kodai Mathematics Journal, Vol. 30, No. 1 (2007), 85–96. http://doi.org/10.2996/kmj/1175287624
  15. The Thurston type theorem for branched coverings of two-sphere. Proceedings of the 4th Internatioanl Congress of Chinese Mathematicans, Higher Education Press, Vol. I (2007), 695–713.
  16. 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
  17. Holomorphic motions and normal forms in complex analysis. Studies in Advanced Mathematics, ICCM2004@2008, AMS/IP, Vol. 42, Part 2 (2008), 457-466.
  18. 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
  19. Liftings of holomorphic maps into Teichmüller spaces (with Sudeb Mitra and Zhe Wang). Kodai Mathematical Journal, 32 (2009), No. 3, 544-560. https://projecteuclid.org/euclid.kmj/1257948895
  20. Holomorphic motions, Fatou linearization, and quasiconformal rigidity for parabolic germs. The Michigan Mathematical Journal, 58 (2009), Issue 2, 517-534. https://doi.org/10.1307/mmj/1250169075
  21. Combinatorial characterization of sub-hyperbolic rational maps (with Gaofei Zhang).  Advances in Mathematics, 221 (2009), 1990–2018. https://doi.org/10.1016/j.aim.2009.03.009
  22. On a question of Katok in one-dimensional case. Discrete and Continuous Dynamical System, Volume 24, Number 4, August 2009, 1209–1213. 10.3934/dcds.2009.24.1209
  23. Asymptotically conformal fixed points and holomorphic motions. Annales Academiæ Scientiarum Fennicæ Mathematica, Volumen 34, 2009, 27–46. http://www.acadsci.fi/mathematica/Vol34/vol34pp27-46.pdf

   2000-2004

63.  Infinitely renormalizable quadratic polynomials. Transactions of American Mathematical Society, 352 (2000), no. 11, 5077-5091. https://doi.org/10.1090/S0002-9947-00-02514-9

64.  On Ruelle-Perron-Frobenius operators. I. Ruelle Theorem (with Aihua Fan). Communications in Mathematical Physics, 223 (2001), 125-141. https://doi.org/10.1007/s002200100538

65.  On Ruelle-Perron-Frobenius operators. II. Convergence Speeds (with Aihua Fan). Communications in Mathematical Physics, 223 (2001), 143-159. https://doi.org/10.1007/s002200100539

  1. Three dimensional partition and infinite renormalization. Proceedings of ICCM2001, Eds. Chang-Shou Lin, Lo Yang, Shing Tung Yau, 2004, 451-482.
  2. Dynamical determinants via dynamical conjugacies for postcritically finite polynomials (with Viviane Baladi and Henrik Rugh). Journal of Statistical Physics, Vol. 108 (2002), Nos. 5/6, 973-993. https://doi.org/10.1023/A:1019783229260

   1995-1999

68.  Renormalization on one-dimensional folding maps.  Dynamical Systems and Chaos, Vol. 1 (1995), 116-125.

69.  Markov partitions and Feigenbaum-like mappings. Communications in Mathematical Physics, 171 (1995), no. 2, 351-363. https://projecteuclid.org/euclid.cmp/1104273566

70.  On Ulam-von Neumann transformations. Communications in Mathematical Physics, 172 (1995), no. 3, 449-459. https://projecteuclid.org/euclid.cmp/1104274310

71.  Smooth classification of geometrically finite one-dimensional maps. Transactions American Mathematical Society, 348 (1996), no. 6, 2391- 2412. https://doi.org/10.1090/S0002-9947-96-01487-0

72.  Transfer operators acting on Zygmund functions (with Viviane Baladi and Oscar Lanford III). Transactions American Mathematical Society, 348 (1996), no. 4, 1599-1615. https://doi.org/10.1090/S0002-9947-96-01599-1

73.  On rigidity of one-dimensional maps. Contemporary Mathematics, American Mathematical Society Series, 211 (1997), 319-431.

74.  Nonlinearity, quasisymmetry, differentiability, rigidity in one-dimensional dynamics. Proceedings of the International Conference in Honor of Professor Liao Shantao,1999, 145-159.

75.  The Julia set of Feigenbaum quadratic polynomial (with Jun Hu). Proceedings of the International Conference in Honor of Professor Liao Shantao, 1999, 99-124.

76.  Liapunov exponents, dual Liapunov exponents and multifractal analysis (with Aihua Fan). Chaos 9 (1999), no. 4, 849—853. http://doi.org/10.1063/1.166468

77.  A proof of existence and simplicity of a maximal eigenvalue for Ruelle-Perron-Frobenius operators. Letters in Mathematical Physics, 48 (1999), no. 3, 211-219. https://doi.org/10.1023/A:1007595323704

78.  Scaling functions, Gibbs measures, and Teichmuller space of circle endomorphisms (with Guizhen Cui and Anthony Quas). Discrete and Continuous Dynamical Systems, Vol. 5 (1999), no. 3, 535-552. 10.3934/dcds.1999.5.535

79.  Geometry of Cantor sets. Transactions American Mathematical Society, 351 (1999), no. 5, 1975-1987. https://doi.org/10.1090/S0002-9947-99-02214-X

  1990-1994

80.  Generalized Ulam-von Neumann transformations. Ph.D. Thesis (1990), Graduate School of CUNY and UMI publication.

81.  Expanding direction of Period Doubling Operator (with Takehiko Morita and Dennis Sullivan). Communications in Mathematical Physics, 144 (1992), no. 3, 509-520. https://projecteuclid.org/euclid.cmp/1104249406

82.  Dynamics of certain non-conformal semigroups.  Complex Variables Theory Applications, 22 (1993), no. 1-2, 27-34. https://doi.org/10.1080/17476939308814643

83.  Asymptotic differentiable structure on Cantor set. Communications in Mathematical Physics, 155 (1993), no. 3, 503-509. https://projecteuclid.org/euclid.cmp/1104253394

84.  Geometry of geometrically finite one-dimensional maps. Communications in Mathematical Physics, 156 (1993), no. 3, 639-647. https://projecteuclid.org/euclid.cmp/1104253720

85.  Towards topological classification of critically finite polynomials (with Sen Hu). Proceedings of Conference on Complex Analysis, International Press, 1994, 132-143.

1985-1989

  1. Density of non-continuity points with infinite entropy (with Lianchao Xu). Scientia Sinica (series A), 28 (1985), no. 10, 1049-1058.

 1980-1984

  1. Restricted problem of motion of three vortices and related topics (with Min Qian). Acta Mathematica Scientia, Vol. 3 (1983), no. 4, 441-453.

 

Books and Proceedings

1.     Renormalization and Geometry in One-Dimensional and Complex Dynamics. Advanced Series in Nonlinear Dynamics, Vol. 10 (1996) World Scientific Publishing Co. Pte. Ltd., River Edge, NJ, xvi+309 pp. ISBN 981-02-2326-9.

2.     Proceedings of the International Conference in Honor of Professor Shantao Liao (with Lan Wen), World Scientific Pub Co, Singapore-New Jersey-London-Hong Kong, 1999, 350 pp.  ISBN: 981024102X.

3.     Complex Dynamics and Related Topics (with Yuefei Wang). New Studies in Advanced Mathematics, the International Press, Somerville, MA, 2004, 501 pp., ISBN:1-57146-121-3.

4.     Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces (with Sudeb Mitra). Contemporary Mathematics Series, American Mathematics Society, Vol. 575, 2012, 375 pp., ISBN-10: 0-8218-5340-6, ISBN-13: 978-0-8218-5340.