# Publications

### Journal Articles

*Nonlocally maximal and premaximal hyperbolic sets*, joint work with Taylor Petty and Sergey Tikhomirov, Contemporary Mathematics, to appear.*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

*Local perturbations of conservative C1-diffeomorphisms,*Joint work with Jerome Buzzi and Sylvain Crovisier, submitted.*Entropy of C1 diffeomorphisms without a dominated splitting ,*Joint work with Jerome Buzzi and Sylvain Crovisier, submitted.*Unique equilibrium states for Bonatti-Viana diffeomorphisms*, joint work with Vaughn Climenhaga and Dan Thompson, submitted.*Unique equilibrium states for Mane diffeomorphisms*, joint work with Vaughn Climenhaga and Dan Thompson, submitted.*Unique equilibrium states for geodesic flows in nonpositive curvature*, joint work with Keith Burns, Vaughn Climenhaga and Dan Thompson, submitted.