Papers
Asymptotics of Transversality in Periodic Curves of Quadratic Rational Maps, 2025. arXiv
With H. Nie, Compactifications and measures for rational maps, 2024. arXiv
With H. Nie, The basin of infinity of tame polynomials, 2022. arXiv
With M. Arfeux, Irreducibility of periodic curves in cubic polynomial moduli space. Proc. Lond. Math. Soc. (3) 127 (2023), no. 3, 792–835.
With H. Nie, Indeterminacy loci of iterate maps in moduli space. Indiana Univ. Math. J. 72 (2023), no. 3, 969–1026.
With A. Esparza-Amador, Oscillating Wandering Domains for p-Adic Transcendental Entire Maps. Bull. Lond. Math. Soc. 54 (2022), no. 6, 2532–2560.
With M. Arfeux, Topological cubic polynomials with one periodic ramification point}, Discrete & Continuous Dynamical Systems - A, (2020), 40, 1799--1811.
Rescaling limits of complex rational maps. Duke Math. J., (2015), 164, 1437--1470.
Leading monomials of escape regions, pp. 103--120 in ``Frontiers in Complex Dynamics: In Celebration of John Milnor’s 80th Birthday'', Editors A. Bonifant, M. Lyubich and S. Sutherland, Princeton University Press 2014.
Puiseux series dynamics of quadratic rational maps, Israel Journal of Math. 201 (2014), no 2, 631--700.
With M. Rees, Counting Hyperbolic Components, Journal of the London Math. Soc. 88 (2013), no 3, 669--698.
With C. Favre and E. Trucco, A non-Archimedean Montel's theorem, Compositio Math. 148 (2012), no 3, 966--990.
With H. Inou, Combinatorics and topology of straightening maps I: compactness and bijectivity. Advances in Math. 231 (2012) no. 5, 2666--2733.
With A. Bonifant, and J. Milnor, On cubic polynomial maps with periodic critical point, Part II: Escape Regions. Conform. Geom. Dyn. 14 (2010) 68--112.
With G. Iommi, The Lyapunov spectrum is not always concave. Journal of Statistical Physics 35 (2009), no.3, 535--546.
Puiseux series polynomial dynamics and iteration of complex cubic polynomials. Ann. Inst. Fourier (Grenoble) 56 (2006), no. 5, 1337--1404.
With R. Bamón, J. Rivera-Letelier and R. Urzúa, On the topology of solenoidal attractors of the cylinder. Annales l'IHP (C) Analyse non linéaire, 23 (2006) 209--236.
Combinatorial continuity in complex polynomial dynamics, Proc. London Math. Soc. Volume 91 Part 1 (July 2005), 215--248.
Real laminations and the topological dynamics of complex polynomials, Adv. in Math. 184 2 (2004), 207--267.
Wandering Orbit Portraits, Trans. Amer. Math. Soc. 254 no. 2 (2002), 1473--1585.
Rational laminations of complex polynomials,in ``Laminations and Foliations in Geometry, Topology and Dynamics'', ed. M. Lyubich, J.W. Milnor, and Y. Minsky, Contemporary Mathematics 269 (2001).
Non-accessible critical points of Cremer polynomials. Ergodic theory and dynamical systems 20 (2000), 1391--1403.
From the Shift Loci to the Connectedness Loci of Complex polynomials, pp 231--245 in ``Complex Geometry of Groups'' (Proceedings of I Iberoamerican Congress on Geometry, Olmué, Chile, January 1998), ed. A. Carocca et al, Contemporary Mathematics 240 (1999).
Other Publications
Appendix A: Rivera Domains, an appendix to L. De Marco, and X. Faber article: Degenerations of complex dynamical systems {II}: analytic and , Math. Ann. 365 (2016), 1694--1699.
``Rational Rays and Critical Portraits of Complex Polynomials''. Ph. D. Thesis, State University of New York (1997). Preprint \#1997/15 IMS SUNY@Stony Brook.
With R. Bam\'on and J. Rivera-Letelier, \marginpar{\sc Unpublished} {\it Wild Lorenz like attractors.} January 2006 version available at arxiv.org/math.DS/0508045