Papers and preprints
in reverse chronological order.
My work is revolves around different classification directions in hyperbolic dynamics.
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 (joint with Tom Farrell) Journal of Topology, 5, no. 2, 276-292 (2012)
k(Diff( S n)) 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)
C (joint with Misha Guysinsky) DCDS-A, 22, no. 1/2, 183-200 (2008) (Pesin Birthday Issue)
1-differentiable conjugacy of Anosov
diffeomorphisms on three dimensional torus Surveys