Papers and preprints

• Local rigidity of Lyapunov spectrum for toral automorphisms (joint with Boris Kalinin and Victoria Sadovskaya) Israel Journal of Mathematics, 238 (2020), no. 1, 389-403.
• Anomalous Anosov flows revisited (joint with Thomas Barthelmé, Christian Bonatti and Federico Rodriguez Hertz) Proceedings of London Math Society, vol. 122 (2021), issue 1, 93-117.
• A numerical study of Gibbs u-measures for partially hyperbolic diffeomorphisms on T³ (joint with Aleksey Kolmogorov and Itai Maimon) Experimental Mathematics, 28 (2019), no. 3, 271–283. For a version with high quality images click here, 17MB file .
• Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence (joint with Christian Bonatti, Andy Hammerlindl and Rafael Potrie) Geometry & Topology, 24-4 (2020), 1751-1790.
• A note on self orbit equivalences of Anosov flows and bundles with fiberwise Anosov flows (joint with Thomas Barthelmé) Mathematical Research Letters, 26 (2019), no. 3, 711-728.
• Surgery for partially hyperbolic dynamical systems I. Blow-ups of invariant submanifolds. Geometry & Topology 22, no. 4, 2219–2252 (2018)
• Aspherical products which do not support Anosov diffeomorphisms (joint with Jean-François Lafont) Ann. Henri Poincaré 17, no. 11, 3005-3026 (2016)
• Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples (joint with Christian Bonatti and Rafael Potrie) Inventiones Mathematicae, 206, no. 3, 801-836 (2016)
• Bootstrap for local rigidity of Anosov automorphisms of the 3-torus Communications in Mathematical Physics, 352, no. 2, 439-455 (2017)
• New partially hyperbolic dynamical systems I (joint with Pedro Ontaneda and Federico Rodriguez Hertz) Acta Mathematica 215, no.2, 363-393 (2015)
• On bundles that admit fiberwise hyperbolic dynamics (joint with Tom Farrell) Mathematische Annalen, 364, no. 1, 401-438 (2016)
• Examples of expanding endomorphisms on fake tori (joint with Tom Farrell) Journal of Topology, 7, no. 3, 805-816 (2014)
• Manifolds with higher homotopy which do not support Anosov diffeomorphisms (joint with Federico Rodriguez Hertz) Bulletin of the London Math Society 46, no. 2, 349-366 (2014)
• The space of Anosov diffeomorphisms (joint with Tom Farrell) Journal of the London Math Society, 89, no. 2, 383-396, (2014)
• Partially hyperbolic diffeomorphisms with compact center foliations Journal of Modern Dynamics, 5, no. 4, 747-767, (2011)
• Local rigidity for Anosov automorphisms (joint with Boris Kalinin and Victoria Sadovskaya; appendix by Rafael de la Llave) Mathematical Research Letters, 18, no. 5, 843-858 (2011)
• Anosov diffeomorphisms constructed from π_k(Diff( Sⁿ)) (joint with Tom Farrell) Journal of Topology, 5, no. 2, 276-292 (2012)
• How typical are pathological foliations in partially hyperbolic dynamics: an example Israel Journal of Mathematics, 187 no. 1, 493-507 (2012)
• Diffeomorphisms Holder conjugate to Anosov diffeomorphisms Ergodic Theory and Dynamical Systems, 30, no. 2, 441-456 (2010)
• Smooth conjugacy of Anosov diffeomorphisms on higher dimensional tori Journal of Modern Dynamics, 2, no. 4, 645-700 (2008)
• C¹-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus (joint with Misha Guysinsky) DCDS-A, 22, no. 1/2, 183-200 (2008) (Pesin Birthday Issue)

Surveys

• Exotic topology in geometry and dynamics (joint with Tom Farrell and Pedro Ontaneda), Handbook of Group Actions (vol. II), Advanced Lectures in Mathematics 32, Higher Education Press & International Press, Beijing-Boston, 3-22 (2015)
• Center Lyapunov exponents in partially hyperbolic dynamics (joint with Ali Tahzibi) Journal of Modern Dynamics, 8, no. 3/4, 549-576 (2014)