Papers and Preprints

With J. Furno and J. Hawkins, Rational families converging to a family of exponential maps, Journal of Fractal Geometry, to appear.

Elliptic Functions with disconnected Julia sets, International Journal of Birfurcation and Chaos, 26, no. 6, (2016).

With J. Clemons, Elliptic functions with connected Julia sets, submitted.

With K. Roy, Dynamics of vertical real rhombic Weierstrass elliptic functions, Involve 10 (2017), No. 3, 361–378.

Differential Equations in Music and Dance, Journal of Mathematics and the Arts, 10 (2016).

Differential Equations in the Visual Arts, submitted.

Fractal Tiling Illustrations of Geometric Series, Proceedings of Bridges 2015, (2015) 423 - 426.

Differential Equations in Literature, Poetry, and Film, Journal of Mathematics and the Arts, 9, Issue 1 - 2 (2015), 1 - 16.

Examples of parametrized families of elliptic functions with empty Fatou sets, New York Journal of Mathematics, 20 (2014), 607-625.

Writing and information literacy in a cryptology first-year seminar, Cryptologia, 38, Issue 3 (2014), 223 - 231.

Sustainability in a Differential Equations Course: A Case Study of Easter Island, International Journal of Mathematical Education in Science and Technology, Vol. 42, Issue 4 (2011), 545 - 553.

With J. Barnes, The Ergodic Theory Carnival, Math. Magazine 83, no. 3 (2010), 180 - 190.

Manipulatives for 3-dimensional coordinate systems, PRIMUS, Vol. 21, no. 4 (2011), 364 - 376.

Cantor Julia sets in a family of even elliptic functions, J. Difference Equ. Appl., 16 no. 5 and 6 (2010), 675 - 688.

With J. Hawkins and J. Kotus, Elliptic functions with critical orbits approaching infinity, J. Difference Equ. Appl. 16 no. 5 and 6 (2010), 613 - 630.

A fundamental dichotomy for Julia sets of a family of elliptic functions, Proc. Amer. Math. Soc. 137 (2009), 3927-3938.

With J. Goldsmith, Dynamical Properties of the Derivative of the Weierstrass Elliptic Function, Involve 2, no.3 (2009), 267 - 288.

With. J. Hawkins,  Connectivity Properties of Julia Sets of Weierstrass Elliptic Functions, Topology and its Applications, Vol. 152, Issues 1-2 ( 2005), 107-137.

With. J. Hawkins,  Parametrized Dynamics of the Weierstrass Elliptic Function, Conf. Geo. and Dyn., 8 (2004), 1 - 35.  pdf .

With. J. Hawkins, Ergodic Properties and Julia Sets of Weierstrass Elliptic Functions,  Monatsh. Math. 137 (2002) 4, 273-300.

With J. Barnes, A Julia Set that is Everything,  Math. Magazine, 76 (2003) 4, 255 - 263.

Ergodic and Bernoulli Properties of Analytic Maps of Complex Projective Space, Trans. Amer. Math. Soc., Vol 354 (2002), 2417-2450.

With J. Barnes, One-Sided Lebesgue Bernoulli Maps of the Sphere of Degree n^2 and 2n^2, Internat. J. Math.  Math. Sci., Vol. 23, No. 6 (2000), 383 - 392.