(with M. Todd) A trichotomy for hitting times and escape rates for a class of unimodal maps, submitted. pdf
(with V. Climenhaga, Y. Lima and H.-K. Zhang) Lyapunov exponents and nonadapted measures for dispersing billiards, Comm. Math. Phys. 405, article 24, (2024). pdf
(with V. Baladi and J. Carrand) Measure of maximal entropy for finite horizon Sinai billiard flows, Annales Henri Lebesgue 7, (2024), 727-747. pdf
(with A. Korepanov) Rates of mixing for the measure of maximal entropy of dispersing billiard maps, Proc. London Math. Soc. 128:1 (2024), e12578. pdf
Topological entropy and pressure for finite horizon Sinai billiards, Proceedings Int. Cong. Math. 2022, Vol. 5, pp. 3432-3459. EMS Press, Berlin, 2023. pdf
(with C. Liverani) Projective cones for sequential dispersing billiards, Comm. Math. Phys. 401:1 (2023), 841-923. pdf
(with V. Baladi) Thermodynamic formalism for dispersing billiards, Journal of Modern Dynamics 18 (2022), 415-493. pdf
Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps, Discrete and Contin. Dynam. Sys. Special issue celebrating 25 years of DCDS, 41:1 (2021), 217-256. pdf
(with M. Todd) Asymptotic escape rates and limiting distributions for multimodal maps, Ergod. Th. and Dynam. Sys. 41:6 (2021), 1656-1705. pdf
(with F. Pene and H.-K. Zhang) Local limit theorem for randomly deforming billiards, Comm. Math. Phys. 375 (2020), 2281-2334. pdf
(with I. Melbourne and M. Nicol) Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas, Nonlinearity 33:8 (2020), 4095-4113. pdf
(with V. Baladi) On the measure of maximal entropy for finite horizon Sinai billiard maps, Journal Amer. Math. Soc. 33:2 (2020), 381-449. pdf
A gentle introduction to anisotropic Banach spaces, Chaos, Solitons and Fractals 116 (2018), 29-42. pdf
(with L. Rey-Bellet and H.-K. Zhang) Fluctuation of the entropy production for the Lorentz gas under small external forces, Comm. Math. Phys. 363:2 (2018), 699-740. pdf
(with H. Bruin and M. Todd) Hitting and escaping statistics: mixing, targets and holes, Advances in Mathematics 328 (2018), 1263-1298. pdf
(with M. Todd) Slow and fast escape for open intermittent maps, Comm. Math. Phys. 351:2 (2017), 775-835. pdf
(with C. Ianzano*, P. Mayer*, P. Morfe*, E. Yoo*) Limiting distributions for countable state topological Markov chains with holes, Discrete and Contin. Dynam. Sys. 37:1 (2017), 105-130. pdf
(with V. Baladi and C. Liverani) Exponential decay of correlations for finite horizon Sinai billiard flows, Inventiones Math. 211:1 (2018), 39-177 pdf. Erratum pdf.
(with M. Todd) Equilibrium states, pressure and escape for multimodal maps with holes, Israel J. Math. 221:1 (2017), 367-424. pdf
(with B. Fernandez) Escape rates and singular limiting distributions for intermittent maps with holes, Trans. Amer. Math. Soc. 368:7 (2016), 4907-4932. pdf
(with H.-K. Zhang) Spectral analysis of hyperbolic systems with singularities, Nonlinearity 27 (2014), 379-433. pdf
Escape rates and physical measures for the infinite horizon Lorentz gas with holes, Dynamical Systems: An International Journal 28:3 (2013), 393-422. pdf
Dispersing billiards with small holes, in Ergodic theory, open dynamics and coherent structures, Springer Proceedings in Mathematics 70 (2014), 137-170. pdf
(with H.-K. Zhang) A functional analytic approach to perturbations of the Lorentz Gas, Communications in Mathematical Physics 324:3 (2013), 767-830. pdf
(with P. Wright) Behavior of the escape rate function in hyperbolic dynamical systems, Nonlinearity 25 (2012), 2133-2150. pdf
(with H.-K. Zhang) Spectral analysis of the transfer operator for the Lorentz Gas, Journal of Modern Dynamics 5:4 (2011), 665-709. pdf
(with P. Wright and L.-S. Young) Entropy, Lyapunov exponents and escape rates in open systems, Ergod. Th. and Dynam. Sys. 32:4 (2012), 1270-1301. pdf
Functional norms for Young towers, Ergod. Th. and Dynam. Sys. 30:5 (2010), 1371-1398. pdf
(with P. Wright and L.-S. Young) Escape rates and physically relevant measures for billiards with small holes, Communications in Mathematical Physics 294:2 (2010), 353-388. pdf
(with H. Bruin and I. Melbourne) Existence and convergence properties of physical measures for certain dynamical systems with holes, Ergod. Th. and Dynam. Sys. 30 (2010), 687-728. pdf
(with M.P. Wojtkowski) A family of pseudo-Anosov maps, Nonlinearity 22 (2009), 1743-1760. Full text pdf Abstract
(with C. Liverani) Stability of statistical properties in two-dimensional piecewise hyperbolic maps, Trans. Amer. Math. Soc. 360:9 (2008), 4777-4814. pdf
(with L.-S. Young) Escape rates and conditionally invariant measures, Nonlinearity 19 (2006), 377-397. pdf
(with L.A. Bunimovich) Deterministic models of the simplest chemical reactions, J. Stat. Phys. 120 (2005), 239-252. pdf
Markov extensions and conditionally invariant measures for certain logistic maps with small holes, Ergod. Th. and Dynam. Sys. 25:4 (2005), 1139-1171. pdf
Markov extensions for dynamical systems with holes: an application to expanding maps of the interval, Israel J. Math. 146 (2005), 189-221. pdf
Thermodynamic Formalism for Dispersing Billiard Maps and Flows, Slides from mini-course given as part of the Summer School on Partial Hyperbolicity, held at the Brin Mathematics
Research Center, University of Maryland, College Park, May 30 - June 9, 2023.
Lecture 1 ∣
Lecture 2 ∣
Lecture 3
Transfer Operators in Hyperbolic Dynamics: An Introduction, with N. Kiamari and C. Liverani, 33° Colóquio Brasileiro de Matemática, IMPA 2021, 252 pp.
Link to IMPA Brazilian Colloquium Book List
Link to pdf on IMPA webpage
Anisotropic Banach Spaces and Thermodynamic Formalism for Dispersing Billiard Maps, Slides from mini-course given as part of the Spring School on Transfer Operators, held during the research semester: Dynamics, Transfer Operators and Spectra, sponsored by the Centre Interfacultaire Bernoulli, EPFL, Lausanne, Switzerland, March 22-26, 2021 (held online).
Lecture 1 ∣
Lecture 2 ∣
Lecture 3 ∣
Lecture 4 ∣
Lecture 5 ∣
Lecture 6
Exponential Decay of Correlations for Contact Hyperbolic Flows, given as a minicourse at the workshop on Statistical Properties of Nonequilibrium Dynamical Systems held at the South University of Science and Technology of China, Shenzhen, China, July 11-26, 2016.
Introductory Lectures on Open Systems, given as part of the LMS-CMI Research School at Loughborough University, UK, April 13-17, 2015.