Publications

- Growth of degree for iterates of rational maps in several variables, with John Erik Fornaess. Indiana University Mathematics Journal,
49(2000), No.2, 751--778.

- Self maps of P^2 with invariant elliptic curves , with Marius Dabija. Complex Manifolds and Hyperbolic Geometry, Contemporary Mathematics
311, (2002), 1--25.

- Contractive Curves, with Marius Dabija. International Journal of Mathematics and Mathematical Sciences,
30(2002), No.4, 227--238.

- Attractors, with John Erik Fornaess. Complex geometry (Gottingen, 2000), 73--84, Springer, Berlin, (2002).

- Elliptic Curves as Attractors in P^2 Part 1: Dynamics, with Marius Dabija and John Milnor. Experimental Mathematics Journal,
16, (2007), No. 4, 385--420.

- Schwarzian Derivatives and Cylinder Maps, with John Milnor. Fields Institute Communications, Vol.
53, 1--21. ``Holomorphic Dynamics and Renormalization'', Lyubich and Yampolsky editors, 2008.

- On Cubic Polynomial Maps with Periodic Critical Orbit, Part II: Escape Regions with Jan Kiwi and John Milnor, Conform. Geom. Dyn.
14(2010), 68--112.

- Errata for ``Cubic Polynomial Maps with Periodic Critical Orbit, PartII: Escape Regions'' with Jan Kiwi and John Milnor, Conform. Geom. Dyn.
14, (2010), 190--193.

- On real and Complex Cubic Curves (with J. Milnor). J. L'Enseignement Mathematique (2) 63, (2017), 21--61. DOI: 10.4171/LEM/63-1/2-2.

- On Antipode Preserving Cubic Maps: the Fjord Theorem, (with X. Buff and J. Milnor). Proc. London Math. Soc. (3) 116 (2018) 670--728. DOI:10.1112/plms.12075

- Group Actions, Divisors, and Plane Curves, (with John Milnor) Bulletin of the American Mathematical Society (2) 57 (2020) 171--267. doi.org/10.1090/bull/1681

- The W. Thurston Algorithm Applied to Real Polynomial Maps (with John Milnor and Scott Sutherland) (arXiv:2005.07800 [math.DS]) Conformal Geometry and Dynamics 25 (2021) 179-199.

- Relations between Escape Regions in the Parameter Space of Cubic Polynomials (with Chad Estabrooks and Thomas Sharland) (arXiv:2205.04994 [math.DS]) Arnold Journal DOI 10.1007/s40598-022-00211-4, published online July 22. 2022. View the paper by clicking here.

Manuscripts

- On Antipode Preserving Cubic Maps II: Tongues and the Ring Locus (with X. Buff and J. Milnor)
in progress

- Elliptic Curves as Attractors in P^2: The Transverse Lyapunov Exponent (with M. Dabija (passed away in 2003) and J. Milnor)
in progress

- On Cubic Polynomial Maps with Periodic Critical Orbit, Part III: External Rays (with J. Milnor)
in progress