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.)

1. The topology of hyperbolic attractors on Compact Surfaces, Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1511-1520.
2. Hyperbolic sets that are not locally maximal , Ergodic Theory and Dynamical Systems, Volume 26, Issue 05, pp 1491-1509.
3. Hyperbolic sets with nonempty interior, Discrete Contin. Dyn. Syst., 15(2):433-446, 2006.
4. On the structure of hyperbolic sets , Ph.D. dissertation, 2004.
5. Blowup in a mass-conserving convection-diffusion equation with superquadratic nonlinearity, with Chris Grant, Proceedings of the American Mathematical Society, 129 (2001), 3353--3362.
6. Qualitative behavior for a nonlinear convection-diffusion equation with conservation, Masters thesis, 1998.

Preprints

1. Quasi-Anosov diffeomorphisms of 3-manifolds, joint work with Jana Rodriquez-Hertz, submitted. (Note: due to problems converting to pdf psfrag replacements do not appear with the figures.)
2. Supergrowth of the number of periodic orbits for non-hyperbolic homoclinic classes, joint work with Christian Bonatti and Lorenzo Diaz. Discrete Contin. Dyn. Syst., to appear.
3. Hyperbolic chain recurrent classes for commuting diffeomorphisms, submitted.
4. Codimension-one attractors for commuting diffeomorphisms, in preparation.
5. Resolving extensions of finitely presented systems, in preparation.

Presentations

1. This is a presentation on hyperbolic dynamics. To view click on Hyperbolic Dynamics to download right click on the link.
2. 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.
3. 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.
4. 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 qad1.pdf.
5. This is a presentation on quasi-Anosov diffeomorphisms of 3-manifoldssuper-exponential growth of periodic points.. This is presentation on 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.