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Acknowledgments
We would like to acknowledge Stanley Tuznik, a former undergraduate complex analysis student, who helped in the early stages of this project. We also thank Professor Russ Howell of Westmont College for giving valuable feedback and suggestions after reviewing our manuscript.
Summary
In this paper, we explore the dynamics of the principal branch of the complex map which has a unique stable fixed point. This function exhibits interesting dynamics, including chaos, making the analysis of this map an excellent case study in an undergraduate complex analysis course or as a supplemental undergraduate research project in such a course. We present several open problems that an undergraduate with a solid complex analysis course would be able to investigate.
Additional information
Notes on contributors
Joseph Previte
Joseph Previte ([email protected], MR ID 635962, ORCID 0000-0002-9465-2426) is an associate professor of mathematics at Penn State Erie, The Behrend College. He did his graduate work at the University of Maryland under the direction of Michael Brin and received his doctorate in 1997. His research interests include mathematical biology, topology, geometry, and dynamical systems. He and his wife have five children. Besides mathematics, he is active in advising the Christian group on campus.
Michelle Previte
Michelle Previte ([email protected], MR ID 714799, ORCID 0000-0002-1916-094X) is an associate professor of mathematics at Penn State Erie, The Behrend College. She earned a B.S. from Westmont College and a Ph.D. from the University of Maryland, College Park in Mathematics. She enjoys running, homeschooling her five children, cheering loudly at their sporting events, and spending time with friends, especially her best friend, her husband, Joe.