Publications
Journal Articles
- Hyperbolic Flows, book published jointly work with Boris Hasselblatt.
- Equilibrium states for certain partially hyperbolic attractors, joint work with Krerley Oiveira, Nonlinearity, to appear.
- Unique equilibrium states for Mane diffeomorphisms, joint work with Vaughn Climenhaga and Dan Thompson, Ergodic Theory Dynam. Systems 39 (2019), no. 9, 2433?2455.
- Unique equilibrium states for geodesic flows in nonpositive curvature, joint work with Keith Burns, Vaughn Climenhaga and Dan Thompson, Geom. Funct. Anal., 28, no. 5, 1209-1259, 2018.
- Unique equilibrium states for Bonatti-Viana diffeomorphisms, joint work with Vaughn Climenhaga and Dan Thompson, Nonlinearity, 31, no. 6, 2532-2570, 2018.
- Entropy of C1 diffeomorphisms without a dominated splitting , Joint work with
Jerome Buzzi and Sylvain Crovisier, Transaction of the AMS, 370, no. 9, 6685-6734, 2018.
- Local perturbations of conservative C1-diffeomorphisms, Joint work with
Jerome Buzzi and Sylvain Crovisier, Nonlinearity, 30, no. 9, 3613-3636, 2017.
- Nonlocally maximal and premaximal hyperbolic sets, joint work with Taylor Petty and Sergey Tikhomirov, Contemporary Mathematics, 692, 83-99, 2017.
- Topological properties of invariant sets for hyperbolic toral automorphisms of surfaces, joint work with Skyler Simmons, Dynamical Systems, 30, no. 1, 23-33, 2015.
- Dynamical coherence for partially hyperbolic diffeomorphisms isotopic to Anosov, joint work with Rafael Potrie and Martin Sambarino, Mathematische Zeitschrift, 278, Issue 1-2, 149-168, 2014.
- Open sets of diffeomorphisms with trivial centralizer in the C1 topology, joint work with Lennard Bakker, Nonlinearity, 27, 2859-2885, 2014.
- Entropic stability beyond partial hyperbolicity, joint work with Jerome Buzzi, Journal of Modern Dynamics, 7, no. 4, 527-552, 2013.
- Resolving extensions of finitely presented systems, Acta Applic. Math., 126, no. 1,131-163, 2013.
- Symbolic extensions for partially hyperbolic dynamical systems with 2-dimensional center bundle, joint work with D. Burguet, Discrete Contin. Dyn. Syst., 33, no. 6, 2253-2270, 2013.
- Entropy-expansiveness for partially hyperbolic diffeomorphisms, joint work with L. J. Diaz, M. J. Pacifico, and J. L. Vieitez, Discrete Contin. Dyn. Syst., 32, no. 12, 4195-4207, 2012.
- Maximal Entropy Measures for certain Partially Hyperbolic, Derived from Anosov systems, joint work with Jerome Buzzi, Martin Sambarino, and Carlos Vasquez, Ergodic Theory and Dynamical Systems, 32, no. 1, 63-79, 2012.
- Symbolic extensions and partially hyperbolic diffeomorphisms, joint work with Lorenzo Diaz, Discrete Contin. Dyn. Syst. 29, no. 4, 1419–1441, 2011.
- Markov partitions for hyperbolic sets, this is joint work with Himal Rathnakumara (an undergraduate student at BYU), Involve, 2(5), 547-555, 2009.
- Quasi-Anosov diffeomorphisms of 3-manifolds, joint work with Jana Rodriquez Hertz, Trans. Amer. Math. Soc., 36, 3707-3720, 2009.
- Trivial centralizers for codimension-one attractors, Bull. Lond. Math. Soc., vol. 41, no. 1, pp 51–56, 2009.
- Trivial centralizers for Axiom A diffeomorphisms, Nonlinearity, 21(11), 2505-2517, 2008.
- Supergrowth of the number of periodic orbits for non-hyperbolic homoclinic classes, joint work with Christian Bonatti and Lorenzo Diaz. Discrete Contin. Dyn. Syst., 20(3):589-604, 2008.
- The topology of hyperbolic attractors on compact surfaces, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1511-1520, 2006.
- Hyperbolic sets that are not locally maximal, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1491-1509, 2006.
- Hyperbolic sets with nonempty interior, Discrete Contin. Dyn. Syst., 15(2):433-446, 2006.
- Blowup in a mass-conserving
convection-diffusion equation with superquadratic nonlinearity,
with Chris Grant, Proceedings of the American Mathematical Society, 129 (2001), 3353--3362.
Other Peer-reviewed Publications
- Uniformly hyperbolic attractors, http://www.scholarpedia.org/article/Uniformly_hyperbolic_attractors
- On the structure of hyperbolic sets , Ph.D. dissertation, 2004.
- Qualitative behavior for a nonlinear convection-diffusion equation with conservation, Masters thesis, 1998.
Preprints
- Centralizers of hyperbolic and kinematic-expansive flows, joint work with Lennard Bakker and Boris Hasselblatt, submitted.
- A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows, joint work with Jerome Buzzi and Ali Tahzibi, submitted.
- Equilibrium states for natural extensions of non-uniformly expanding local homeomorphisms, joint work with Krerley Oliveira, submitted.
- Accessibility and centralizers for partially hyperbolic flows, joint work with Boris Hasselblatt, submitted.
- Phase Transitions for geodesic flow on rank one surfaces, joint work with Keith Burns, Jerome Buzzi, and Noelle Sawyer, in preparation.