Joanna Furno

Department of Mathematics

University of Houston

Office: PGH 636

Email: jfurno@math.uh.edu

My primary research interests are in ergodic theory and dynamical systems, especially on *p*-adic and Berkovich spaces. My current work examines the ergodic properties and orbit equivalence classes of *p*-adic transformations. My interests for future work include analogues of results from complex dynamics and applications to arithmetic dynamics. For more information on my current research, see my research statement.

- "Bounded remainder sets for rotations on the adelic torus," with Alan Haynes and Henna Koivusalo. Submitted. (2018). https://arxiv.org/abs/1803.10559
- "Rational families converging to a family of exponential maps," with Jane Hawkins and Lorelei Koss.
*Journal of Fractal Geometry*. To appear. (2017). - "Everywhere divergence of the one-sided ergodic Hilbert transform for circle rotations by Liouville numbers,” with David Constantine.
*New York Journal of Mathematics*.**23**(2017), 273-294. http://nyjm.albany.edu/j/2017/23-14.html - "Haar measures and Hausdorff dimensions of
*p*-adic Julia sets."*Ergodic Theory, Dynamical Systems, and the Continuing Influence of John C. Oxtoby, Contemporary Mathematics*.**678**(2016), 187-196. - "Approximations for
*p*-adic transitive isometries."*Topology Proceedings*.**46**Oct. 2015, 323-338. - "Singular
*p*-adic transformations for Bernoulli product measures."*New York Journal of Mathematics.***20**(2014), 799-812. http://nyjm.albany.edu/j/2014/20-40.html - "Orbit equivalence of
*p*-adic transformations and their Iterates."*Monatshefte für Mathematik***175**(2014), no. 2, 249-276.

- "Natural extensions for
*p*-adic beta shifts and other scaling maps." - "Relating singularly perturbed rational maps to families of entire maps," with Lorelei Koss.

- "Ergodic Theory of
*p*-adic Transformations," Ph.D. Thesis, University of North Carolina at Chapel Hill, May 2013. Carolina Digital Repository

The following papers contain research that I participated in as an undergraduate. The first paper was completed as part of an REU at Oregon State University. The last two papers are on research completed while I worked in Kerry Kuehn's physics lab at Wisconsin Lutheran College.

- Furno, Joanna and Patrick Waters. “Investigations Regarding Partitions and Multipartitions.” Proceedings of the Research Experiences for Undergraduates Program in Mathematics, Oregon State University, Summer 2007.

REU Proceedings.

- Furno, Joanna and Kerry Kuehn. “Tidal Pattern Instabilities on Multi-moon Planets.” Icarus, Vol. 189, Issue 1, Jul. 2007, 246-255.

- Kuehn, Kerry, Jonathan Polfer, Joanna Furno, and Nathan Finke. “Apparatus for Real-time Acoustic Imaging of Rayliegh-Bénard Convection.” Review of Scientific Instruments, Vol. 78, Issue 11, Nov. 2007.