Research Papers - De-Jun Feng (Updated Aug 11, 2022).

  1. A separation property for iterated function systems of similitudes. Preprint, 2022. (with Huo-Jun Ruan and Ying Xiong)

  2. Dimension of invariant measures for affine iterated function systems. Preprint, 2019. To appear in Duke Math. J.

  3. Dimension estimates for $C^1$ iterated function systems and repellers. Part II. To appear in Ergodic theory Dynam. Systems (with Karoly Simon)

  4. Dimension estimates for $C^1$ iterated function systems and repellers. Part I. To appear in Ergodic theory Dynam. Systems (with Karoly Simon)

  5. Estimates on the dimension of self-similar measures with overlaps. J. Lond. Math. Soc. 105 (2022), no. 4, 2104--2135. (with Zhou Feng)

  6. On arithmetic sums of fractal sets in ${\Bbb R}^d$. J. Lond. Math. Soc. 104(2021), no. 1, 35-65. (with Yufeng Wu)

  7. Dimensions of random statistically self-affine Sierpinski sponges in $\mathbb R^k$. J. Math. Pure. Appl. 149 (2021), 254--303. (with Julien Barral)

  8. On multifractal formalism for self-similar measures with overlaps. Math. Z. 298 (2021), no. 1-2, 359--383. (with Julien Barral)

  9. On the Hausdorff Dimension of Bernoulli Convolutions Int. Math. Res. Not. IMRN. 2020 (2020), no. 19, 6569--6595. (with Shigeki Akiyama, Tom Kempton and Tomas Persson)

  10. Uniformity of Lyapunov exponents for non-invertible matrices. Ergodic theory Dynam. Systems 40 (2020), no. 9, 2399-2433. (with Chiu-Hong Lo and Shuang Shen)

  11. Affine embeddings of Cantor sets and dimension of $\alpha\beta$-sets. Israel J. Math. 226 (2018), no. 2, 805--826. (with Ying Xiong)

  12. Self-affine sets in analytic curves and algebraic surfaces Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 1, 109--119. (with Antti Kaenmaki)

  13. Dimensions of random covering sets in Riemann manifolds Ann. Probab. 46 (2018), no. 3, 1542--1596. (with Esa Jarvenpaa, Maarit Jarvenpaa and Ville Suomala)

  14. Projections of planar Mandelbrot measures Adv. Math. 325(2018), 640--718. (with Julien Barral)

  15. Variational principles for weighted topological pressure. J. Math. Pure. Appl. 106 (2016), 411--452. (with Wen Huang)

  16. On the topology of polynomials with bounded integer coefficients. J. Eur. Math. Soc. 18 (2016), no. 1, 181--193.

  17. Self-similar subsets of Cantor sets. Adv. Math. 281 (2015), 857--885. (with Hui Rao and Yang Wang)

  18. Affine embeddings and intersections of Cantor sets J. Math. Pures Appl. 102 (2014), no. 6, 1062--1079. (with Wen Huang and Hui Rao)

  19. Non-conformal repellers and the continuity of pressure for matrix cocycles Geom. Funct. Anal. 24 (2014), 1101--1128. (with Pablo Shmerkin)

  20. Partition functions in numeration systems with bounded multiplicity. Uniform Distribution Theory 9 (2014), 43--77. (with Pierre Liardet and Alan Thomas)

  21. Local conical dimensions for measures. Math. Proc. Cambridge Philos. Soc., 154 (2013), 465--479 (with Antti Kaenmaki and Ville Suomala)

  22. Multifractal formalism for almost all self-affine measures. Comm. Math. Phys., 318 (2013), 473--504 (with Julien Barral)

  23. Variational principles for topological entropies of subsets. Journal of Functional Analysis 263 (2012) 2228--2254 (with Wen Huang)

  24. Weighted thermodynamic formalism on subshifts and applications. Asian J. Math. 16 (2012), 319--352. (with Julien Barral)

  25. Multifractal analysis of Bernoulli convolutions associated with Salem numbers. Adv. Math. 229 (2012), 3052--3077.

  26. Non-uniqueness of ergodic measures with full Hausdorff dimensions on a Gatzouras-Lalley carpet. Nonlinearity 24 (2011), 2563--2567. (with Julien Barral)

  27. Equilibrium states of the pressure function for products of matrices Discrete Contin. Dyn. Syst. 30 (2011), 699--708. (with Antti Kaenmaki)

  28. Growth rate for Beta expansions. Monatsh. Math. 162 (2011), 41--60. (with Nikita Sidorov)

  29. Equilibrium states for factor maps between subshifts. Adv. Math. 226 (2011) 2470--2502

  30. Lyapunov spectrum of asymptotically sub-additive potentials. Comm. Math. Phys. 297 (2010), 1--43 (with Wen Huang)

  31. On the Structures of Generating Iterated Function Systems of Cantor Sets. Adv. Math. 222 (2009) 1964--1981 (with Yang Wang)

  32. Dimension theory of iterated function systems. Comm. Pure Appl. Math. 62 (2009), 1435--1500 (with Huyi Hu)

  33. Multifractal formalism for Self-similar measures with weak separation condition. Journal de Mathematiques Pures et Appliquees 92 (2009), 407--428 (with Ka-Sing Lau)

  34. Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages. Ergodic theory and dynamical systems. 29 (2009), 885--918. (with Lin Shu)

  35. Lyapunov exponents for products of matrices and Multifractal analysis. Part II: General matrices. Israel J. of Math. 170 (2009), 355-394

  36. The thermodynamic formalism for sub-additive potentials. Discrete Contin. Dyn. Syst. 20 (2008), 639-657 (with Yong-Luo Cao and Wen Huang)

  37. When is the union of two unit intervals a self-similar set satisfying the open set condition? Monatsh. Math. 152 (2007), 125-134 (with Su Hua and Yuan Ji)

  38. Refinable functions with non-integer dilations. J. Func. Anal. 250 (2007), 1-20 (with Xin-Rong Dai and Yang Wang)

  39. Structure of refinable splines. Applied and Computational Harmonic Analysis 22 (2007): 374-381 (with Xin-Rong Dai and Yang Wang)

  40. Gibbs properties of self-conformal measures and the multifractal formalism. Ergodic theory and Dynamical Systems. 27 (2007), 787-812

  41. Classification of Refinable Splines. Constr. Approx. 24 (2006): 187-200 (with Xin-Rong Dai and Yang Wang)

  42. Generation of Finite Tight Frames by Householder Transformations. Adv. Comput. Math. 24 (2006): 297-309 (with Long Wang and Yang Wang)

  43. A Class of Self-Affine Sets and Self-Affine Measures. J. Four. Anal. Appl. 11 (2005), 107-124. (with Yang Wang)

  44. The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers. Adv. Math. 195 (2005), 24-101. Old Version in 1999: Part (I). Part (II).

  45. On statistical framework for estimation from random set observations. J. Theoret. Probab. 17 (2004) 85-110 (with Ding Feng)

  46. Bernoulli convolution associated with non-Pisot numbers. Adv. Math. 187 (2004), 173-194 (with Yang Wang)

  47. The variational principle for products of non-negative matrices. Nonlinearity 17 (2004) 447--457.

  48. Lyapunov exponent for products of matrices and Multifractal analysis. Part I: Positive matrices. Israel J. of Math., 138 (2003), pp. 353--376.

  49. Multifractal Analysis of the Weak Gibbs Measures and phase transition--application to some Bernoulli convolutions. Ergodic Theory & Dynamical System 23 (2003) 1751--1784 (with Eric Olivier)

  50. The smoothness of $L^q$-spectrum of self-similar measures with overlaps. J. Lond. Math. Soc. . 68 (2003), no. 1, 102--118.

  51. The exact packing measure of linear Cantor sets. Math. Nachr. 248-249(2003), 102--103.

  52. Convolutions of equicontractive self-similar measures on the line. Illinois Journal of Mathematics. 46 (2002), no. 4, 1339--1351.(with Nhu T. Nguyen and Tonghui Wang)

  53. On a property of Pisot numbers. J. Number Theory. 97 (2002), 305--316 (with Zhi-Ying Wen)

  54. Pressure Function for Products of Non-negative Matrices. Math. Research Lett. 9 (2002), no. 2-3, 363--378. (with Ka-Sing Lau)

  55. Ergodic limits on the conformal repeller. Adv. Math. 169 (2002) 58-91. (with Ka-Sing Lau and Jun Wu)

  56. Comparing Hausdorff measures and packing measures on the line, Math. Nachr. 241 (2002), 65--72.

  57. Recurrence, dimension and entropy, J. Lond Math Soc. 64 (2001), no. 1, 229--244. (with Ai-Hua Fan and Jun Wu)

  58. The Hausdorff dimension of recurrent sets in symbolic spaces, Nonlinearity, 14(2001), 81-85. (with Jun Wu)

  59. On the distribution of long-term time averages on symbolic space, J. Statist. Phys, 99(2000), 813-856. (with Ai-Hua Fan)

  60. The pointwise densities of Cantor measure, J. Math. Anal. Appl., 250(2000), 692-705. (with Su Hua and Zhi-Ying Wen)

  61. Some relations between packing premeasure and packing measure, Bull. London Math. Soc., 31 (1999), 665-670 (with Su Hua and Zhi-Ying Wen)

  62. On the limit Rademacher functions and Bernoulli convolutions, Dynamical Systems, Proceedings of the International Conference in Honor of Professor Liao Shantao, World Scientific, Singapore, 1999, pp. 46--49

  63. Analyse multifractale de la recurrence sur l'espace symbolique, C. R. Acad. Sci. Paris Ser. I Math. 327(1998), 629-632. (with Ai-Hua Fan)

  64. Category and dimension of compact subsets of ${\bf R}^n$, Chinese Sci. Bull. 42(1997), 1680-1683. (With Jun Wu).

  65. The net measure properties of symmetric Cantor sets and their applications, Progr. Natur. Sci., 7(1997), 172-178. (With Hui Rao and Jun Wu)

  66. Some dimensional results for homogeneous Moran sets, Sci. China Ser. A, 40(1997), 475-482. (With Zhi-Ying Wen and Jun Wu)

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