# Publications

- Toral band Fatou components for the Weierstrass P function, with L. Koss, AMS Contemporary Math 797, 203 – 218 (2024).
- Single and double toral band Fatou components in meromorphic dynamics, with L. Koss, Conform. Geom. Dyn., 27 (2023) 118-144. (journal version)
- Unbounded Fatou components for elliptic functions over square lattices, with M. Moreno Rocha, Houston Journal of Math 47 (2021), No. 2, 353-374.
- Stability of Cantor Julia sets in the space of iterated elliptic functions, AMS Contemporary Math 736 Dynamical Systems and Random Processes, (2019) 69-97. (Hawkins_ContMath)
- The maximal entropy measure of Fatou boundaries, with M. Taylor, Disc. and Cts. Dyn. Sys, Vol. 38, 9, (2018), 4421-4431. (Hawkins_Taylor)
- A Special Class of Infinite measure-preserving Quadratic rational maps, with R. Bayless-Rossett, online July 22, (2018), Dyn. Sys 34 (2019) 2, 218-233.(Bayless-Rossetti_Hawkins)
- Rational families converging to an exponential family of maps, with J. Furno and L. Koss, Journal of Fractal Geometry 6 (2019), 1, 89-109 (furno_hawkins_koss).
- An Experimental View of Herman Rings for Dianalytic maps of RP^2 , with M. Randolph, (2017) arXiv:1706.09880, 1-24
- Dynamics and Julia Sets of Iterated Elliptic Functions, with M. Moreno Rocha, New York J. of Math. 24 (2018) 947- 979. (NYJM_Hawkins_Moreno-Rocha)
- Nondeterministic and Stochastic Cellular Automata and Virus Dynamics, with E. Burkhead,

J. Cellular Automata (2018), 1-2, 103–119.(Burkhead_Hawkins) - Lebesgue measure theoretic dynamics of rational maps, Contemporary Math 678, Amer. Math. Soc., (2016) 197–217.(Hawkins_Oxtoby_Proc)
- Markov process models of the dynamics of HIV reservoirs, Math. Biosci., 275, (2016) 18-24 (Hawkins_HIV_Markov)
- A cellular automaton model of Ebola virus dynamics, with E. Burkhead, Physica A, 438 (2015), 424-435.(Burkhead_Hawkins_PhysicaA)
- Markov cellular automata models for chronic disease, with D. Molinek, Intl. J. of Biomathematics Vol. 8, No. 6 (2015), 1 –22. (Hawkins_Molinek)
- Topological dynamics of dianalytic maps on Klein surfaces, Topology Proceedings 46 (2015) 339–353.(Hawkins_TopProc_2015)
- Julia sets on RP2 and dianalytic dynamics, with S. Goodman, Conf. Geom. and Dyn. 18 (2014), 95-120.(Goodman_Hawkins_CGDS)
- Proof of a Folklore Julia set Connectedness Theorem and Elliptic Functions, Conf. Geom. and Dyn. Sys,

Conform. Geom. Dyn. 17 (2013), 26-38 (Hawkins_CGDS) - Ergodic and chaotic properties of Lipschitz maps on smooth surfaces, with S. Goodman, NYJM, 18 (2012), 95-120 (Goodman_Hawkins_NYJM1), Corrections and errata in NYJM: (Goodman_Hawkins_errata)
- Dynamics of a family of degree 3 rational maps with no period 2 orbits, with R. Hagihara, Intl. Jour. of Bif. and Chaos, Vol. 21, No. 11 (2011), 3323-3339. (Hagihara_Hawkins)
- Families of Ergodic Type III_0 Ergodic Transformations in Distinct Orbit Equivalence Classes, with A. Dooley and D. Ralston, Monat. fur Math, 164, (2011), 4, 369-381.(dooley_hawkins_ralston)
- Parameter space for the Weierstrass P function with square period lattice, with M. McClure, Intl. Jour. of Bifurcation and Chaos. Vol. 21, No. 1 (2011), 125-135.(hawk-mccl-2011)
- Elliptic functions with critical orbits approaching infinity, with L. Koss, Lorelei and J. Kotus,
*J. Difference Equ. Appl.*16 (2010), no. 5-6, 613–630. (hawkins-k-k-JDEA) - A family of elliptic functions with Julia set the whole sphere.
*J. Difference Equ. Appl.*16 (2010), no. 5-6, 597–612. (hawkins-JDEA-1) - Rigidity of smooth one-sided Bernoulli endomorphisms, with Henk Bruin,
*New York J. Math.*15 (2009), 451–483. (Bruin_Hawkins_NYJM) - A dynamical study of a cellular automata model of the spread of HIV in a lymph node, with E. Burkhead and D. Molinek,
*Bull. Math. Biol.*71 (2009), no. 1,25–74.(Burkhead_Hawkins_Molinek) - One-dimensional stochastic cellular automata, with D. Molinek,
*Topology Proc.*31 (2007), no. 2, 515–532. (hawkins-molinek) - Families of ergodic and exact one-dimensional maps, with J. Barnes,
*Dyn. Syst.*22 (2007), no. 2, 203–217. (barnes-hawkins) - Smooth Julia sets of elliptic functions for square rhombic lattices. Spring Topology and Dynamical Systems Conference.
*Topology Proc.*30 (2006), no. 1,265–278.(hawkins-topproc-06) - Locally Sierpinski Julia sets of Weierstrass elliptic ℘ functions, with D. Look,
*Internat. J. Bifur. Chaos Appl. Sci. Engrg.*16 (2006), no. 5, 1505–1520.(Hawkins_Look) - Connectivity properties of Julia sets of Weierstrass elliptic functions, with L. Koss,
*Topology Appl.*152 (2005), no. 1-2, 107–137. (hawkins-koss-topapp) - Parametrized dynamics of the Weierstrass elliptic function, with L. Koss,
*Conform. Geom. Dyn.*8 (2004), 1–35. (hawkins-koss-cdg) - Lebesgue ergodic rational maps in parameter space,
*Internat. J. Bifur. Chaos Appl. Sci. Engrg.*13 (2003), no. 6, 1423–1447 - Maximal Entropy Measure for rational maps and a random iteration algorithm for Julia sets, with M. Taylor,
*Internat. J. Bifur. Chaos Appl. Sci. Engrg.*13 (2003), no. 6, 1423–1447 (appendix only). (This is a re-texed version of the appendix, which is hard to obtain.) - Ergodic properties and Julia sets of Weierstrass elliptic functions, with L. Koss,
*Monatsh. Math.*137 (2002), no. 4, 273–300. (hawkins-koss-topapp) - McMullen’s root-finding algorithm for cubic polynomials.
*Proc. Amer. Math. Soc.*130 (2002), no. 9, 2583–2592. (Hawkins_ProcAMS_2002) - Exactness and maximal automorphic factors of unimodal interval maps with H. Bruin,
*Ergodic Theory Dynam. Systems*21 (2001), no. 4, 1009–1034. (bruin-hawkins-etds) - Examples and properties of nonexact ergodic shift measures, with S. Eigen,
*Indag. Math. (N.S.)*10 (1999), no. 1, 25–44. (eigen-hawkins-indag) - Examples of expanding C1 maps having no σ-finite invariant measure equivalent to Lebesgue, with H. Bruin,
*I**srael J. Math.*108 (1998), 83–107. (bruin-hawkins-isr) - Characterizing mildly mixing actions by orbit equivalence of products, with C. Silva,
*New York J. Math.*3A (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9–13, 1997, 99–115. (hawkins-silva-nyjm) - A construction of a non-measure-preserving endomorphism using quotient relations and automorphic factors, with K. Dajani,
*J. Math. Anal. Appl.*204 (1996), no. 3, 854–867 (dajani-hawkins-jmaa) - Amenable relations for endomorphisms.
*Trans. Amer. Math. Soc.*343 (1994), no. 1, 169–191. (hawkins-tams) - Examples of natural extensions of nonsingular endomorphisms, with K. Dajani,
*Proc. Amer. Math. Soc.*120 (1994), no. 4, 1211–1217. (dajani-hawkins-procams) - Rohlin factors, product factors, and joinings for n-to-one maps, with K. Dajani,
*Indiana Univ. Math. J.*42 (1993), no. 1, 237–258. (dajani-hawkins-iumj) - Noninvertible transformations admitting no absolutely continuous σ-finite invariant measure, with C. Silva.
*Proc. Amer. Math. Soc.*111 (1991), no. 2, 455–463. (hawkins_silva_PAMS) - Diffeomorphisms of manifolds with nonsingular Poincaré flows.
*J.**Math. Anal. Appl.*145 (1990), no. 2, 419–430. (Hawkins_JMAA_1990) - Properties of ergodic flows associated to product odometers.
*Pacific J. Math.*141 (1990), no. 2, 287–294.(Hawkins_PJM_1990) - Ratio sets of endomorphisms which preserve a probability measure.
*Measure and measurable dynamics (Rochester, NY, 1987),*159–169, Contemp. Math., 94,*Amer. Math. Soc., Providence, RI,*1989.(Hawkins_CMAMS_ratiosets) - Remarks on recurrence and orbit equivalence of nonsingular endomorphisms, with C. E. Silva,
*Dynamical systems (College Park, MD, 1986–87),*281–290, Lecture Notes in Math., 1342,*Springer, Berlin,*1988.(Hawkins_Silva_recurrence_1987) - Approximately transitive (2) flows and transformations have simple spectrum, with E. A. Robinson, Jr.,
*Dynamical systems (College Park, MD, 1986–87),*261–280, Lecture Notes in Math., 1342,*Springer, Berlin,*1988. (Hawkins_Robinson_AT(2)) - Abelian cocycles for nonsingular ergodic transformations and the genericity of type III1 transformations, with J. Choksi and V. S. Prasad,
*Monatsh. Math.*103 (1987), no. 3, 187–205. (Choksi1987_AbelianCocyclesForNonsingularE) - Smooth T^n-valued cocycles for ergodic diffeomorphisms.
*Proc. Amer. Math. Soc.*93 (1985), no. 2, 307–311. (Hawkins_cocycles) - Approximately transitive diffeomorphisms of the circle, with E. J. Woods,
*Proc. A**mer. M**ath. Soc.*90 (1984), no. 2, 258–262. (Hawkins_Woods_PAMS) - Smooth type III diffeomorphisms of manifolds.
*Trans. Amer. Math. Soc.*276 (1983), no. 2, 625–643. (Hawkins_TAMS1983) - Non-ITPFI diffeomorphisms.
*Israel J. Math.***42**(1982), no. 1-2, 117–131. (Hawkins1982_Non-itpfidiffeomorphisms) - On C2-diffeomorphisms of the circle which are of type III_1, with K. Schmidt,
*Invent. Math.***66**(1982), no. 3, 511–518. (Hawkins-Schmidt1982_OnC2-diffeomorphismsOfTheCircl)