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