Publications

(Click on a title to get the corresponding .pdf file. Note that because of font embedding, these files average around a half a megabyte apiece.)

Journal Articles

  1. 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 (2012), no. 1, 63-79.
  2. Symbolic extensions and partially hyperbolic diffeomorphisms, joint work with Lorenzo Diaz, Discrete Contin. Dyn. Syst. 29 (2011), no. 4, 1419–1441
  3. Markov partitions for hyperbolic sets, this is joint work with Himal Rathnakumara (an undergraduate student at BYU), Involve, 2(5), 547-555, 2009.
  4. Quasi-Anosov diffeomorphisms of 3-manifolds, joint work with Jana Rodriquez Hertz, Trans. Amer. Math. Soc., 36, 3707-3720, 2009.
  5. Trivial centralizers for codimension-one attractors, Bull. Lond. Math. Soc., vol. 41, no. 1, pp 51–56, 2009.
  6. Trivial centralizers for Axiom A diffeomorphisms, Nonlinearity, 21(11), 2505-2517, 2008.
  7. 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.
  8. The topology of hyperbolic attractors on compact surfaces, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1511-1520, 2006.
  9. Hyperbolic sets that are not locally maximal, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1491-1509, 2006.
  10. Hyperbolic sets with nonempty interior, Discrete Contin. Dyn. Syst., 15(2):433-446, 2006.
  11. 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. Resolving extensions of finitely presented systems, Acta Applic. Math., to appear.
  2. Entropy-expansiveness for partially hyperbolic diffeomorphisms, joint work with L. J. Diaz, M. J. Pacifico, and J. L. Vieitez, Discrete Contin. Dyn. Syst., to appear.
  3. Entropic stability beyond partial hyperbolicity, joint work with Jerome Buzzi, preprint.
  4. Symbolic extensions for partially hyperbolic dynamical systems with 2-dimensional center bundle, joint work with D. Burguet, preprint.
  5. Cohomology for expanding hyperbolic attractors, joint work with Greg Conner and Jana Rodriquez Hertz, preprint.
  6. Intrinsic characterizations for premaximal hyperbolic sets, joint work with Sergey Tikhomirov, in preparation.
  7. Topological properties of invariant sets for Anosov maps with holes, joint work with Skyler Simmons, in preparation.

Presentations

  1. This is a presentation I gave at a conference in Rio on partially hyperbolicity. The talk is on symbolic extensions for partially hyperbolic dynamics. Click on phsymbext.pdf.
  2. This is a colloquium I gave on entropy. Click on entropycolloq011210.pdf.
  3. Here is a presentation on dynamical systems that I give to undergraduates. Click on dynsysundergrad.pdf. I usually also show the following two youtube cips http://www.youtube.com/watch?v=Whvl6CikDxA and http://www.youtube.com/watch?v=Qe5Enm96MFQ. This one is also quite fun http://www.youtube.com/watch?v=vuyRCfhCZT0&NR=1
  4. Here is a presentaiton on symbolic extensions for partially hyperbolic systems. This is joint work with L. Diaz, M. Pacifico, and J. Vieitez. To download right click on symbext.pdf.
  5. This is presentation on measures of maximal entropy for certain robustly transitive diffeomorphisms. This work was done jointly with J. Buzzi, M. Sambarino, and C. Vasquez. To download right click on maxentropya.pdf.
  6. This is a presentation I gave to graduate students at a summer school in China. The talk is meant to be an overview of robust transitivity. To download right click on robust.pdf.
  7. This is a presentation on quasi-Anosov diffeomorphisms of 3-manifolds. This is presentation on joint work with Jana Rodriguez-Hertz. After downloading it go to view and select full screen to view the best. To download right click on qad-ams.pdf.
  8. This is a presentation on super-exponential growth of periodic points.. This is joint work with Christian Bonatti and Lorenzo Diaz. After downloading it go to view and select full screen to view the best. To download right click on super.pdf.
  9. This is a presentation on hyperbolic attractors. After downloading it go to view and select full screen to view the best. To download right click on attractors.pdf.
  10. This is a presentation on hyperbolic dynamics. To view click on Hyperbolic Dynamics to download right click on the link.
  11. This is a presentation on hyperbolic sets. It is a rather large (4M) pdf file. After downloading it go to view and select full screen to view the best. To download right click on Hyperbolic Sets.