Research

My main research interest is holomorphic dynamics. In particular, I study topological and combinatorial descriptions of parameter and dynamical planes for entire and meromorphic maps.

Published articles

Unbounded Fatou components for elliptic functions over square lattices

With J. Hawkins. To appear in Houston Journal of Mathematics, 2021.

Carathèodory convergence for Leau and Baker domains.

With A. Esparza-Amador. Dynamical Systems, 36:2, 256-276, 2021. Online version.

Herman rings of elliptic functions.

Arnold Mathematical Journal 6, 551-570, 2020. PDF.

Rational maps with bad reduction and domains of quasiperiodicity

With V. Nopal-Coello, Actas T1, Colección Papiros, UNAM, 13-31, 2020. PDF

Dynamics and Julia sets of iterated elliptic functions

With J.M. Hawkins, New York Journal of Mathematics, 24, 947-979, 2018. PDF

Families of Baker domains for meromorphic functions with countable many essential singularities

With A. Esparza-Amador. Journal of Difference Equations and Applications, 23, 1869-1883, 2017. PDF

A class of even elliptic maps with no Herman rings

With P. Pérez Lucas. Topology Proc., 48, 151-162, 2016. PDF

Modeling and finite-time walking control of a biped robot with feet

With Juan E. Machado and Héctor M. Becerra. Mathematical Problems in Engineering, Volume 2015, 1-17, 2015. PDF

A combinatorial invariant for escape time Sierpinski rational maps

Fundamenta Mathematicae, 222, 99-130, 2013. PDF

Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps

With A. Garijo and X. Jarque. Fundamenta Mathematicae, 214, 2, 135-160, 2011. PDF

Joining polynomial and exponential combinatorics for some entire maps.

With A. Garijo and X. Jarque. Publicacions Matemátiques, 54, 1, 113-136, 2010. PDF

Singular perturbations of $z^n$

With R.L. Devaney et al. Transcendental dynamics and complex analysis, Eds. P. Rippon and G. Stallard, Cambridge University Press, 111-137, 2008. PDF

Rational maps with generalized Sierpinski gaskets as Julia sets

With R.L. Devaney and S. Siegmund. Topol. App., 154 (1): 11-27, 2007. PDF

Sierpinski curves and gaskets as Julia sets of rational maps

With P. Blanchard et al. Dynamics on the Riemann Sphere, EMS, 97-119, 2006. PDF

Indecomposable continua and Misiurewicz points in exponential dynamics

With R.L. Devaney and X. Jarque. Intl. J. Bif. Chaos, 15 (10): 3281-3293, 2005. PDF

Playing catch-up with iterated exponentials

With Devaney et al. Amer. Math. Monthly, 111 (8): 704-709, 2004. PDF

Existence of indecomposable continua for unstable exponentials

Top Proc, 27 (1): 233-244, 2003. PDF

Geometry of the antennas in the Mandelbrot set

With R.L. Devaney. Fractals, 10 (1): 39-46, 2002. PDF

A semilinear model for exponential dynamics and topology

With R.L. Devaney. Top. Proc., 26 (1): 153-167, 2001/2002. PDF

Accessible points in the Julia set of stable exponentials

With R. Bhattacharjee et al. Disc. Cont. Dyn. Syst. B, 1 (3): 299-318, 2001. PDF

Preprints

Satellite parabolic perturbations in exponential dynamics

With A. Benini.

Rational maps with bad reduction and domains of quasiperiodicity

With V. Nopal-Coello. Arxiv version.

Other publications

Mexican mathematicians abroad: recent contributions

Coeditor, with F. Galaz and N. Bárcenas. Contemporary Mathematics, Volume 657, 2016, 237 pp.