Publications

Journal Articles

  1. Nonlocally maximal and premaximal hyperbolic sets, joint work with Taylor Petty and Sergey Tikhomirov, Contemporary Mathematics, to appear.
  2. Topological properties of invariant sets for hyperbolic toral automorphisms of surfaces, joint work with Skyler Simmons, Dynamical Systems, 30, no. 1, 23-33, 2015.
  3. 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.
  4. Open sets of diffeomorphisms with trivial centralizer in the C1 topology, joint work with Lennard Bakker, Nonlinearity, 27, 2859-2885, 2014.
  5. Entropic stability beyond partial hyperbolicity, joint work with Jerome Buzzi, Journal of Modern Dynamics, 7, no. 4, 527-552, 2013.
  6. Resolving extensions of finitely presented systems, Acta Applic. Math., 126, no. 1,131-163, 2013.
  7. 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.
  8. 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.
  9. 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.
  10. Symbolic extensions and partially hyperbolic diffeomorphisms, joint work with Lorenzo Diaz, Discrete Contin. Dyn. Syst. 29, no. 4, 1419–1441, 2011.
  11. Markov partitions for hyperbolic sets, this is joint work with Himal Rathnakumara (an undergraduate student at BYU), Involve, 2(5), 547-555, 2009.
  12. Quasi-Anosov diffeomorphisms of 3-manifolds, joint work with Jana Rodriquez Hertz, Trans. Amer. Math. Soc., 36, 3707-3720, 2009.
  13. Trivial centralizers for codimension-one attractors, Bull. Lond. Math. Soc., vol. 41, no. 1, pp 51–56, 2009.
  14. Trivial centralizers for Axiom A diffeomorphisms, Nonlinearity, 21(11), 2505-2517, 2008.
  15. 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.
  16. The topology of hyperbolic attractors on compact surfaces, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1511-1520, 2006.
  17. Hyperbolic sets that are not locally maximal, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1491-1509, 2006.
  18. Hyperbolic sets with nonempty interior, Discrete Contin. Dyn. Syst., 15(2):433-446, 2006.
  19. 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

  1. Uniformly hyperbolic attractors, http://www.scholarpedia.org/article/Uniformly_hyperbolic_attractors
  2. On the structure of hyperbolic sets , Ph.D. dissertation, 2004.
  3. Qualitative behavior for a nonlinear convection-diffusion equation with conservation, Masters thesis, 1998.

Preprints

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