An ergodic spectral decomposition theorem for singular star flows (with M.J. Pacifico and J. Yang). Submitted.
arXiv.
An improved Climenhage-Thompson criterion for locally maximal sets (with M.J. Pacifico, J. Yang and Gongran Yao). Submitted.
arXiv.
An example derived from the Lorenz attractor (with M. Li, J. Yang and R. Zheng). Submitted.
arXiv.
Equilibrium states for the classical Lorenz attractor and sectional-hyperbolic attractors in higher dimensions (with M.J. Pacifico and J. Yang).
Duke Math. J., 174 (2025) no. 10, 1901--2010.
Published Version or arXiv
Shub's example revisited (with C. Liang, R. Saghin and J. Yang).
Ergodic Theory and Dynamical Systems, 45 (2025), no. 3, 894–914.
Published Version or arXiv
Maximal transverse measures of expanding foliations (with R. Ures, M. Viana and J. Yang).
Comm. Math. Phys., 405 (2024), no. 5, Paper No. 121, 40 pp.
Published Version or arXiv.
Thermodynamical u-formalism I: maximal u-entropy measures for maps that factor over Anosov (with R. Ures, M. Viana and J. Yang).
Ergodic Theory and Dynamical Systems, 44 (2024), no. 1, 290–333.
Published version or arXiv.
An entropy dichotomy for generic singular star flows (with M.J. Pacifico and J. Yang).
Trans. Amer. Math. Soc., 376 (2023), 6845–6871.
Published version or arXiv.
Existence and uniqueness of equilibrium states for systems with specification at a fixed scale (with M.J. Pacifico and J. Yang).
Nonlinearity, 35 (2022), Number 12.
Published version or arXiv.
A countable partition for singular flows, and its application on the entropy theory (with Y. Shi and J. Yang).
Israel J. Math, 249 (2022), 375–429.
Published version or arXiv.
Escape rate and conditional escape rate from a probabilistic point of view (with C. Davis and N. Haydn).
Ann. Henri Poincaré, 22 (2021), 2195–2225.
Published version or arXiv.
Statistical properties of physical-like measures (with S. Gan, J. Yang and R. Zheng)
Nonlinearity, 34 (2021), 1014–1029.
Published version or arXiv.
Rare event process and entry times distribution for arbitrary null sets on compact manifolds.
Ann. Inst. Henri Poincaré, Probab. Stat. 57 (2021), no. 2, 1103-1135.
Published version or arXiv.
Entropy theory for sectional hyperbolic flows (with M.J. Pacifico and J. Yang).
Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 38 (2021), 1001-1030.
Published version or arXiv.
Geometric law for numbers of returns until a hazard under φ-mixing (with Y. Kifer).
Israel J. Math. 244 (2021), 319-357.
Published version or arXiv.
Exponential law for random maps on compact manifolds (with J. Rousseau and N. Haydn).
Nonlinearity, 33 (2020), 6760–6789.
Published version or arXiv.
A new criterion of physical measures for partially hyperbolic diffeomorphisms (with Y. Hua and J. Yang).
Trans. Amer. Math. Soc. 373 (2020), no. 1, 385-417.
Published version or arXiv.
Local escape rate for φ-mixing dynamical systems (with N. Haydn).
Ergodic Theory and Dynamical Systems. 40 (2020), no. 10, 2854-2880.
Published version or arXiv.
Hitting times distribution and extreme value law for semi-flows (with M.J. Pacifico).
Discrete Contin. Dyn. Syst. series A, 37 (2017), no. 11, 5861-5881.
Published version or arXiv.
A derivation of the Poisson law for returns of smooth maps with certain geometrical properties (with N. Haydn).
Dynamical systems, ergodic theory, and probability: in memory of Kolya Chernov, 141-160, Contemp. Math., 698, Amer. Math. Soc., Providence, RI, 2017.
Published version or arXiv.
Entry times distribution for dynamical balls on metric spaces (with N. Haydn).
J. Stat. Phys. 167 (2017), no. 2, 297-316.
Published version or arXiv.
Entry times distribution for mixing systems (with N. Haydn).
J. Stat. Phys. 163 (2016), no. 2, 374-392.
Published version or arXiv.
A countable partition for singular flows based on filtration structure: construction and application (with M. Li, J. Yang and R. Zheng)
We construct a countable partition for flows with hyperbolic singularities such that its metric entropy for invariant probability measures is uniformly bounded. As an application, we show the upper semi-continuity of the entropy map for singular flows away from homoclinic tangencies. The construction is based on a filtration structure on the Grassmanian manifold and improves [8] above.
Limiting return times distribution for arbitrary null sets until one encounters an obstacle (with N. Haydn).
"About the exciting story of the intrepid random traveler and how many times he returned home before being swallowed by a black hole, forever vanishing from the face of the earth."
In this paper we study the number of entries to a neighborhood U ('home') of some measure zero set, before the orbit enters another open set V (a black hole). Assuming that the system has sufficient mixing property, we show that the number of entries converges in distribution to a compound Poisson distribution with an exponentially distributed stopping time.
Uniqueness of equilibrium states for Lorenz attractors in any dimension (with M.J. Pacifico and J. Yang).
This is a research announcement for [4] above.
arXiv.
Decay of correlations for maximal measure of maps derived from Anosov (with J. Yang).
This paper has been merged into [6] and [7] above as an example. In this paper we proved that the unique measure of maximal entropy for any 3-dimensional DA diffeomorphism has exponential decay of correlations.
arXiv.