Publications by Jane Hawkins
Hawkins' Home Page
Research papers since 1993 - in some cases the final version appears at the
journal site and not here due to subscription embargos.
- The Maximal Entropy Measure of Fatou Boundaries
, with M. Taylor, (2017) arXiv:1706.09880, 1-15.
- An Experimental View of Herman Rings for Dianalytic maps of RP^2
, with M. Randolph, (2017) arXiv:1706.09880, 1-24.
- A Special Class of Infinite Measure-Preserving Quadratic Rational Maps
, with R. Bayless, Preprint, 2017.
- Dynamics and Julia sets of iterated elliptic functions, with M. Moreno Rocha, Preprint, 2016.
- Rational families converging to a family of exponential maps , with J. Furno and L.Koss, Journal of Fractal Geometry (2017), to appear.
- Nondeterministic and stochastic cellular automata
and virus dynamics, with E. Burkhead, Journal of Cellular Automata, Vol. 12 (2017), to appear.
- Lebesgue measure theoretic dynamics of rational maps , Ergodic theory, dynamical systems, and the continuing influence of John C. Oxtoby, 197–217, Contemp. Math., 678, Amer. Math. Soc., Providence, RI, (2016).
- Markov process models of the dynamics of HIV, Math Biosci. 275 (2016), 18-24.
- A cellular
automaton model of Ebola virus dynamics, with E. Burkhead, Physica A, 438 (2015), 424-435.
- Markov cellular automata
models for chronic disease, with D. Molinek, Intl. J. of
Biomathematics Vol. 8, No. 6 (2015), 1- 22.
- Topological dynamics of dianalytic maps on Klein surfaces, Top.Proc 46 (2015) 339-353.
Sets on RP2 and Dianalytic Dynamics, with S.
Goodman, Conf. Geom. and Dynamics 18 (2014) 85-109.
of a Folklore Julia Set Connectedness Theorem and Connections with
Elliptic Functions , Conf. Geom. and Dyn, Vol.17, 26-38 (2013).
(Link to related graphics.)
- Ergodic and chaotic
properties of Lipschitz maps on smooth surfaces ,
with S. Goodman, New York J. Math 18 (2012) 95-120.
- Errata and corrigenda:
Ergodic and chaotic properties of Lipschitz maps on smooth surfaces, with S. Goodman, New York J. Math 18
and bifurcations of a family of rational maps with parabolic fixed points , with R. Hagihara,
Intl. J. of Bif. and Chaos, 21, No. 11, (2011) 3323-3339.
- Families of type III_0 ergodic
transformations in distinct orbit equivalent classes ,
with A. Dooley and D. Ralston, Monat. fur Math, Volume 164, Number 4, (2011), 369-381.
dynamics for the Weierstrass elliptic function
over square period lattices , with M.
McClure, Internat. J. Bifur. Chaos Appl. Sci. Engrg, 21 (2011), no. 1, 125–135.
family of elliptic functions with Julia set the whole sphere , J. Difference Eqn. Appl. 16 (2010),
no. 5-6, 597-612.
Elliptic functions with critical orbit approaching infinity,
with L. Koss and J. Kotus, J. Difference Equ Appl. 16 (2010), no. 5-6, 613-630.
- Rigidity of
Smooth one-sided Bernoulli Endomorphisms, with H. Bruin, New York Journal of Math, 15, (2009), 451-483.
dynamical study of a cellular automata model of the spread of HIV in a
lymph node, with E. Burkhead and D. Molinek,
Bulletin of Mathematical Biology (2009) 71: 25-74.
dimensional stochastic cellular automata ,
with D. Molinek, Topology Proc. 31 (2007), No.
of Ergodic and Exact One-Dimensional Maps, with J. Barnes, Dynamical
Systems: an International Journal, Vol. 22, No. 2, (2007), 203-217.
Julia sets of elliptic functions for square rhombic lattices, Spring
Topology and Dynamical Systems Conference. Topology Proc. 30 (2006), no.
Sierpinsk Julia sets of Weierstrass
elliptic P functions, with Daniel Look, Intl. Jour. of Bifurcation and
Chaos, Vol. 16, No. 5 (2006) 1505-1520.
- Connectivity Properties of Julia sets of Weierstrass Elliptic Functions, with L. Koss,
Topology and its Appl 152 (2005) 107-137 .
Dynamics of the Weierstrass Elliptic Function , with L. Koss, Conf. Geom. Dyn. 8 (2004), 1-35.
- Lebesgue Ergodic Parameters for
Quadratic Rational Maps, Intl. J. of Bifurcation and Chaos, Vol. 13, No.
6, 1423-1442, June,(2003).
- Maximal Entropy Measure for Rational Maps
and a Random Iteration Algorithm, with Michael E. Taylor, Intl. J. of
Bifurcation and Chaos, Vol. 13, No. 6, 1442-1448, June (2003).
Properties and Julia sets of Weierstrass
Elliptic Functions, with L. Koss, Monatsh.
Math. 137, 273-300, (2002).
Root-Finding Algorithm for Cubic Polynomials, Proc. AMS 130, 2583-2592
and Maximal Automorphic Factors of S-Unimodal Maps, with H. Bruin,
Erg. Theory and Dyn. Sys. 21, Part 4, (2001),
of expanding C^1 maps having no sigma-finite measure equivalent to
Lebesgue, with H. Bruin, Isr. J. Math. 108, 83-107 (1999)
- Examples and Properties of Nonexact Ergodic Shift Measures, with S. Eigen, Indag. Mathem.,N.S.,10(1), 25-44 (1999)
Mildly Mixing Actions by Orbit Equivalence of Products, with C. Silva,
New York J. Math, 3A , 99-115 (1998).
- A Construction of a Non-Measure Preserving
Endomorphism Using Quotient Relations and Automorphic Factors, with K.
Dajani, J. Math. Anal. and Appl. 204, 854-867
Relations for Endomorphisms, Trans. AMS,
343, 169-191 (1994).
- Examples of Endomorphisms
and their Natural Extensions, with K. Dajani ,
Proc. AMS, 120, 1211-1217 (1994).
- Rohlin Factors,
Product Factors, and Joinings for n-to-one Maps,
with K. Dajani, Ind. Univ. Math. J., 42, 237-258 (1993).
- Mathematica Made Easy, Course
notes and manual, 1997.
- The Basics of Complex Dynamics,
Short course notes , 1-26, 2000.
- Linear Algebra for Differential
Equations, Course notes, exercises, and solns,
- Ergodic Theory, (an entry in Encylcopedia of Noninear
Science) , Routledge Publishing, NY.
- How I Became a Mathematician, Bob
Ryan's 2002 Almanac and Guide for the Weatherwise , NBC4 Washington, DC, (pdf format) .
- Casting Light on the Shadow of
Doubt, book review on James Franklin's The Science of Conjecture, Science ,
Vol.294, Oct. 19, 2001, p.527, PDF format or PS format or full
text for subscribed members to Science.
OTHERS RELATING TO MY WORK
computer labs give students the big picture, by Kevin O'Kelly, The
Chapel Hill News, May 10, 1998
by Nature, by Angela Spivey, Endeavors:Research
and Creativity, UNC, Fall, 2000
Up, by Steve Adams and Kevin O'Kelly, Carolina Alumni Review, September/October,
- by Kevin O'Kelly, The
University Gazette, August 16, 2000.