Research papers

Preprints

1. Thermodynamic formalism for non-compact systems with expansivity and specification
     - with Daniel J. Thompson and Tianyu Wang.

2. Every finite horizon Sinai billiard map has a unique measure of maximal entropy
     - with Jason Day.

3. A nonstationary Ruelle-Perron-Frobenius theorem
     - with Gregory Hemenway.

4. Maximizing entropy for power-free languages
   
   

Published papers

5. Gibbs measures have local product structure
   Proceedings of the American Mathematical Society, 153, 10 (2025), 4315-4326

6. Equilibrium measures for two-sided shift spaces via dimension theory
     - with Jason Day.
   Ergodic Theory and Dynamical Systems, 45, 2 (2025), 427-466

7. Lyapunov exponents and nonadapted measures for dispersing billiards
     - with Mark Demers, Yuri Lima, and Hongkun Zhang.
   Communications in Mathematical Physics, 405, 24 (2024)

8. SRB and equilibrium measures via dimension theory
   in A Vision for Dynamics in the 21st Century: The Legacy of Anatole Katok (2024), pp. 94-138, Cambridge.

9. Closed geodesics on surfaces without conjugate points
     - with Gerhard Knieper and Khadim War.
   Communications in Contemporary Mathematics, 24 (2022) No. 06, 2150067.

10. SRB measures and Young towers for surface diffeomorphisms
      - with Stefano Luzzatto and Yakov Pesin.
    Annales Henri Poincaré, 23 (2022), 973-1059

11. Beyond Bowen's specification property
    (Survey) - with Daniel J. Thompson.
    in Thermodynamic Formalism (2021), pp. 3-82, Springer Lecture Notes in Mathematics Vol. 2290, CIRM Jean-Morlet Chair subseries

    • A small correction is needed in the proofs of two propositions.

12. Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points
      - with Gerhard Knieper and Khadim War.
    Advances in Mathematics, 376 (2021), 107452.

13. Equilibrium measures for some partially hyperbolic systems
      - with Yakov Pesin and Agnieszka Zelerowicz.
    Journal of Modern Dynamics, 16 (2020), 155-205.

    • The published version has a minor error in the proof of Lemma 6.6.

14. Positive entropy equilibrium states
      - with Van Cyr.
    Israel Journal of Mathematics, 232 (2019), no. 2, 899-920.

15. One-sided almost specification and intrinsic ergodicity.
    - with Ronnie Pavlov.
    Ergodic Theory and Dynamical Systems, 39 (2019), 2456-2480.

16. Equilibrium states for Mañé diffeomorphisms.
      - with Todd Fisher and Daniel J. Thompson.
    Ergodic Theory and Dynamical Systems, 39 (2019), 2433-2455.

17. Equilibrium states in dynamical systems via geometric measure theory
    (Survey) - with Yakov Pesin and Agnieszka Zelerowicz.
    Bulletin of the American Mathematical Society, 56 (2019), no. 4, 569-610.

18. Specification and towers in shift spaces.
    Communications in Mathematical Physics, 364, issue 2 (2018), 441-504.

19. Unique equilibrium states for geodesic flows in nonpositive curvature.
      - with Keith Burns, Todd Fisher, and Daniel J. Thompson.
    Geometric and Functional Analysis, 28 (2018), no. 5, 1209-1259.

20. Unique equilibrium states for Bonatti-Viana diffeomorphisms.
      - with Todd Fisher and Daniel J. Thompson.
    Nonlinearity, 31 (2018), no. 6, 2532-2570.

21. Large deviations for systems with non-uniform structure.
    - with Daniel J. Thompson and Kenichiro Yamamoto.
    Transactions of the American Mathematical Society, 369 (2017), no. 6, 4167-4192.

    • • Condition [A.1] in Theorems A and B needs to be strengthened slightly.

22. The geometric approach for constructing Sinai-Ruelle-Bowen measures
    (Survey) - with Stefano Luzzatto and Yakov Pesin.
    Journal of Statistical Physics, 166 (2017), 467-493.

23. Building thermodynamics for non-uniformly hyperbolic maps
    (Survey) - with Yakov Pesin.
    Arnold Mathematical Journal, 3 (2017), 37-82.

24. Unique equilibrium states for flows and homeomorphisms with non-uniform structure.
      - with Daniel J. Thompson.
    Advances in Mathematics, 303 (2016), 745-799.

25. Non-stationary non-uniform hyperbolicity: SRB measures for non-uniformly hyperbolic attractors.
      - with Dmitry Dolgopyat and Yakov Pesin.
    Communications in Mathematical Physics, 346, issue 2 (2016), 553-602.

26. Hadamard-Perron theorems and effective hyperbolicity.
      - with Yakov Pesin.
    Ergodic Theory and Dynamical Systems, 36 (2016), 23-63.

27. Intrinsic ergodicity via obstruction entropies.
      - with Daniel J. Thompson.
    Ergodic Theory and Dynamical Systems, 34 (2014), 1816-1831.

28. The thermodynamic approach to multifractal analysis.
    Ergodic Theory and Dynamical Systems, 34 (2014), 1409-1450.

29. Topological pressure of simultaneous level sets.
    Nonlinearity 26 (2013), 241-268.

30. Equilibrium states beyond specification and the Bowen property.
      - with Daniel J. Thompson.
    Journal of the London Mathematical Society 87 (2013), 401-427.

31. Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors.
      - with Daniel J. Thompson.
    Israel Journal of Mathematics, 192 (2012), 785-817.

    • Two corrections: one to Theorem B, one regarding S-gap shifts and almost specification

32. Bowen's equation in the non-uniform setting.
    Ergodic Theory and Dynamical Systems 31 (2011), 1163-1182.

33. Multifractal formalism derived from thermodynamics for general dynamical systems.
    Electronic Research Announcements in Mathematical Sciences 17 (2010), 1-11.

34. A note on two approaches to the thermodynamic formalism.
    Discrete and Continuous Dynamical Systems 27 (2010), 995-1005.

35. Open problems in the theory of non-uniform hyperbolicity
    (Survey) - with Yakov Pesin.
    Discrete and Continuous Dynamical Systems, 27 (2010), 589-607.