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Publications: in some cases a revised version has been published.

Publications

  1. Toral band Fatou components for the Weierstrass P function, with L. Koss, submitted.
  2. Single and double toral band Fatou components in meromorphic dynamics, with L. Koss, to appear, Conf. Geom and Dynamics, accepted 2022.
  3. Unbounded Fatou components for elliptic functions over square lattices, with M. Moreno Rocha,  Houston Journal of Math 47 (2021), No. 2, 353-374.
  4. 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)
  5. The maximal entropy measure of Fatou boundaries, with M. Taylor, Disc. and Cts. Dyn. Sys, Vol. 38, 9, (2018), 4421-4431. (Hawkins_Taylor)
  6. 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)
  7. 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).
  8. An Experimental View of Herman Rings for Dianalytic maps of RP^2 , with M. Randolph, (2017) arXiv:1706.09880, 1-24
  9. 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)
  10. Nondeterministic and Stochastic Cellular Automata and Virus Dynamics, with E. Burkhead,
    J. Cellular Automata (2018), 1-2, 103–119.(Burkhead_Hawkins)
  11. Lebesgue measure theoretic dynamics of rational maps, Contemporary Math 678, Amer. Math. Soc., (2016) 197–217.(Hawkins_Oxtoby_Proc)
  12. Markov process models of the dynamics of HIV reservoirs, Math. Biosci., 275, (2016) 18-24 (Hawkins_HIV_Markov)
  13. A cellular automaton model of Ebola virus dynamics, with E. Burkhead, Physica A, 438 (2015), 424-435.(Burkhead_Hawkins_PhysicaA)
  14. Markov cellular automata models for chronic disease, with D. Molinek, Intl. J. of Biomathematics Vol. 8, No. 6 (2015), 1 –22. (Hawkins_Molinek)
  15. Topological dynamics of dianalytic maps on Klein surfaces, Topology Proceedings 46 (2015) 339–353.(Hawkins_TopProc_2015)
  16. Julia sets on RP2 and dianalytic dynamics, with S. Goodman, Conf. Geom. and Dyn. 18 (2014), 95-120.(Goodman_Hawkins_CGDS)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. 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)
  24. Rigidity of smooth one-sided Bernoulli endomorphisms, with Henk Bruin,  New York J. Math. 15 (2009), 451–483. (Bruin_Hawkins_NYJM)
  25.  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)
  26. One-dimensional stochastic cellular automata, with D. Molinek, Topology Proc. 31 (2007), no. 2, 515–532. (hawkins-molinek)
  27. Families of ergodic and exact one-dimensional maps, with J. Barnes, Dyn. Syst. 22 (2007), no. 2, 203–217. (barnes-hawkins)
  28. 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)
  29. 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)
  30. Connectivity properties of Julia sets of Weierstrass elliptic functions, with L. Koss,  Topology Appl. 152 (2005), no. 1-2, 107–137. (hawkins-koss-topapp)
  31. Parametrized dynamics of the Weierstrass elliptic function, with L. Koss, Conform. Geom. Dyn. 8 (2004), 1–35.  (hawkins-koss-cdg)
  32. Lebesgue ergodic rational maps in parameter space, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no. 6, 1423–1447
  33. 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.)
  34. Ergodic properties and Julia sets of Weierstrass elliptic functions, with L. Koss, Monatsh. Math. 137 (2002), no. 4, 273–300. (hawkins-koss-topapp) 
  35. McMullen’s root-finding algorithm for cubic polynomials. Proc. Amer. Math. Soc. 130 (2002), no. 9, 2583–2592. (Hawkins_ProcAMS_2002)
  36. 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)
  37. Examples and properties of nonexact ergodic shift measures, with S. Eigen,  Indag. Math. (N.S.) 10 (1999), no. 1, 25–44.  (eigen-hawkins-indag)
  38. Examples of expanding C1 maps having no σ-finite invariant measure equivalent to Lebesgue, with H. Bruin, Israel J. Math. 108 (1998), 83–107. (bruin-hawkins-isr)
  39. 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)
  40. 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)
  41. Amenable relations for endomorphisms. Trans. Amer. Math. Soc.343 (1994), no. 1, 169–191. (hawkins-tams)
  42. Examples of natural extensions of nonsingular endomorphisms, with K. Dajani, Proc. Amer. Math. Soc. 120 (1994), no. 4, 1211–1217. (dajani-hawkins-procams)
  43. 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)
  44. 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)
  45. Diffeomorphisms of manifolds with nonsingular Poincaré flows. J. Math. Anal. Appl. 145 (1990), no. 2, 419–430. (Hawkins_JMAA_1990)
  46. Properties of ergodic flows associated to product odometers.Pacific J. Math. 141 (1990), no. 2, 287–294.(Hawkins_PJM_1990)
  47. 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)
  48. 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)
  49. 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))
  50. 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)
  51. Smooth T^n-valued cocycles for ergodic diffeomorphisms. Proc. Amer. Math. Soc. 93 (1985), no. 2, 307–311. (Hawkins_cocycles)
  52. Approximately transitive diffeomorphisms of the circle, with E. J. Woods, Proc. Amer. Math. Soc. 90 (1984), no. 2, 258–262. (Hawkins_Woods_PAMS)
  53. Smooth type III diffeomorphisms of manifolds. Trans. Amer. Math. Soc. 276 (1983), no. 2, 625–643. (Hawkins_TAMS1983)
  54. Non-ITPFI diffeomorphisms. Israel J. Math. 42 (1982), no. 1-2, 117–131. (Hawkins1982_Non-itpfidiffeomorphisms)
  55. 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)
Other publications.