Research

I study dynamical systems, a branch of modern mathematics concerned with the time evolution of natural and iterative processes.  I am particularly interested in theoretical and practical applications of chaotic and nonlinear systems in the physical sciences.

My current research examines connections between quantum and chaotic entanglement.  My main analytical tool is a chaotic system's set of cupolets, which are highly-accurate approximations to its unstable periodic orbits.  I am also developing new techniques for analyzing the differential geometry of strange attractors, as well as new ways to hierarchically order the cupolets of these systems.

For more information, see my vita.

Publications

1. Cupolets: History, Theory, and Applications (with K. M. Short), Dynamics, 4(2), 394-424 (2024).

2. The Euclidean Discus Toss (with M. Smith), PRIMUS, 33(10), 1071-1090 (2023).

3. Chaotic entanglement: entropy and geometry (with K.M. Short), Entropy, 23(10), 1254 (2021).

4. Fundamental cupolets of chaotic systems (with K. M. Short), Chaos, 30(9), 093114 (2020).

5. Signatures of quantum mechanics in chaotic systems (with K. M. Short), Entropy, 21(6), 618 (2019).

6. Video Made the Calculus Star (with S. Smith and R. Talbert), PRIMUS, 29(1), 43-55 (2019).

7. On the potential for entangled states between chaotic systems (with K. M. Short), International Journal of Bifurcation and Chaos, 24(104), 1450077 (2014).

8. Controlled transitions between cupolets of chaotic systems (with K. M. Short and E. Cooke), Chaos, 24(1), 013110 (2014).

9. Predicting attenuant and resonant 2-cycles in periodically forced discrete-time two-species population models (with J.E. Franke), Journal of Biological Dynamics, 6(2), 782-812 (2012).

Patents

• Systems and methods for chaotic entanglement using cupolets (with K. M. Short), U.S. Patent No. 11,354,381 (2022).

• Systems and methods for chaotic entanglement using cupolets (with K. M. Short), U.S. Patent No. 10,754,919 (2020).

• Systems and methods for chaotic entanglement using cupolets (with K. M. Short), U.S. Patent No. 9,824,065 (2017).