# Jeffrey A. Diller

### Professor

Department Chair

B.A., University of Dayton, 1988

Ph. D., University of Michigan, 1993

Email: Diller.1@nd.edu

Office: 255B Hurley Hall

Phone: (574) 631-7083

Fax: (574) 631-6579

For additional information see Jeffrey Diller’s Personal Page.

**Research Interests**

I study multi-variable complex dynamics. Using tools from pluripotential theory, complex algebraic geometry and dynamical systems, my goal is to understand the behavior of rational maps of two or more variables under iteration. So far, I have mostly concentrated on the case of plane birational maps, and this work has led to a general probabilistic picture for the dynamics of such maps. I am currently interested in extending this picture to higher dimensions and non-invertible rational maps. I am also interested in understanding the dynamics of particular examples in much greater detail, and to this end I have done enough computer experimentation that I now find fascinating even the programming aspects of understanding dynamical systems.

**Selected Publications**

- J. Diller, R. Dujardin and V. Guedj. Dynamics of meromorphic maps with small topological degree I-III, preprints.

- J. Diller, D. Jackson, and A. Sommese. Invariant curves for birational surface maps. Transactions of the
*American Mathematical Society*359 (2007), pages 2793—2991.

- E. Bedford and J. Diller. Real and complex dynamics of a family of birational maps of the plane: the golden mean subshift,
*American Journal of Mathematics*127 (2005), pages 595-646.

- E. Bedford and J. Diller. Energy and invariant measure for birational surface maps.
*Duke Mathematical Journal*128 (2005), pages 338-368.

- J. Diller and C. Favre. Dynamics of Bimeromorphic Maps of Kahler surfaces.
*American Journal of Mathematics*123 (2001), pages 1135-1169.

Please direct questions and comments to: Diller.1@nd.edu