Selected/Recent Publications by Jane Hawkins
Hawkins' Home Page
Research papers - in some cases the final version appears at the journal site and not here
- A family of elliptic functions with Julia set the whole sphere , to appear, Journal of Diff. Eqn and App..
- Elliptic functions with critical orbit approaching infinity, with L. Koss and J. Kotus, to appear, Jour. of Diff. Eqn. and App.
- Rigidity of Smooth one-sided Bernoulli Endomorphisms, with H. Bruin, New York Journal of Math, 15, 2009.
- A 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.
- One dimensional stochastic cellular automata , with D. Molinek, Topology Proc. 31 (2007), No. 2, 515-532.
- Families of Ergodic and Exact One-Dimensional Maps, with J. Barnes, Dynamical Systems: an International Journal, Vol. 22, No. 2, (2007), 203-217.
- Smooth Julia sets of elliptic functions for square rhombic lattices, Spring Topology and Dynamical Systems Conference. Topology Proc. 30 (2006), no. 1, 265--278.
- Locally Sierpinski 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 .
- Parametrized 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).
- Ergodic Properties and Julia sets of Weierstrass
Elliptic Functions, with L. Koss,
Monatsh. Math. 137, 273-300, (2002).
- McMullen's Root-Finding Algorithm for Cubic Polynomials,
Proc. AMS 130, 2583-2592 (2002)
- Exactness and Maximal
Automorphic Factors of S-Unimodal Maps,
with H. Bruin, Erg. Theory and Dyn. Sys. 21, Part
4, (2001), 1009-1034.
- Examples 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)
-
Characterizing 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 (1996).
-
Amenable 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).
COURSE NOTES:
-
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, 2001.
For a general audience:
- 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.
ARTICLES BY OTHERS RELATING TO MY WORK
-
Math
computer labs give students the big picture, by Kevin O'Kelly, The
Chapel Hill News, May 10, 1998
-
Numbers
by Nature , by Angela Spivey, Endeavors:Research and Creativity, UNC,
Fall, 2000
-
Powering
Up, by Steve Adams and Kevin O'Kelly, Carolina Alumni Review, September/October,
2000.
-
Summer workshops help instructors prepare for CCI, by Kevin O'Kelly, The University Gazette, August 16, 2000.