__Publications:__

1. Geodesic flow on the two-sphere, Part I:
Positive measure entropy, Ergod. Th. & Dynam.
Sys. 8 (1988),
531-553.

2. Geodesic flow on the two-sphere, Part II:
Ergodicity, Dynamical Systems, Springer Lecture Notes in Math.,
Vol. 1342 (1988), 112-153.

__ __

3. Using integrability to produce chaos:
billiards with positive entropy, Comm. Math. Phys. 141 (1991),
225-257.

4. Joint with C. Liverani,
Potentials on the two-torus for which the Hamiltonian flow is
ergodic, Commun. Math. Phys. 135 (1991), 267-302.

5, Physical
examples of linked twist maps with chaotic dynamics in Twist Mappings
and Their Applications, R. McGehee and K. Meyer, Eds, Springer-Verlag (1993).

6. Transverse Homoclinic
Connections for Geodesic Flows, Hamiltonian Dynamical Systems: History, Theory
and Applications, H.S. Dumas, K.R. Meyer and D.S. Schmidt, Eds,
Springer-Verlag (1995), 115-125.

7.
Elliptic
islands in generalized Sinai billiards, Ergod. Th. & Dynam. Sys. (1996), 16, 975-1010.

8. Joint with K. Burns, Embedded surfaces with
ergodic geodesic flow, Inter. J. of Bifurcation and Chaos, Vol. 7, No. 7 (1997)
1509-1527.

9. Non-ergodicity of two particles interacting
via a smooth potential, J. of Statistical Physics, Vol. 96, Nos. 5/6 (1999)
1021-1048.

10.
Chaotic geodesic motion: an extension of M.C. Escher’s Circle Limit Design, pp.
318-

333, M.C. Escher's Legacy: A Centennial Celebration Schattschneider,
Doris; Emmer, Michele (Eds.) 2003, Springer-Verlag, (refereed publication).

11. Joint with C. Pugh, Anosov geodesic flows
for embedded surfaces,
Astérisque 287

(2003), 61-69 in
Geometric methods in Dynamics II - Volume in honor of
Jacob

Palis, W. de Melo, M.Viana, J.C. Yoccoz (Ed.)

12.
Creating transverse homoclinic connections in planar
billiards, *Zap**. Nauchn. Sem. S.- *

* Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 300 (2003), Teor.* Predst.
Din. Sist. Spets.

Vyp. 8, 122--134, 287.

13. Joint with C. Pugh,
Finite horizon Riemann Structures and Ergodicity, Ergod. Th. & Dynam.
Sys. (2004) 24, 89 - 106.

14. Perspectives on
Mathematics Education Projects in a Service-Learning Framework, in

Mathematics in Service to the Community,
MAA Notes #66, Charles Hadlock editor, 2005.

15. Destroying ergodicity in geodesic flows on surfaces,
Nonlinearity 19 (2006) 149-169.

16.
Joint with A. Root and J. Zaebst, Changing Pedagogies Course: a study of the effectiveness
of a new course in recruiting STEM majors into education.

__Expository:__

1. I think, therefore I
sum, Bryn Mawr Alumnae Bulletin, Fall 1991.

·
The
Topology and Geometry of the Costa surface, a 5 minute video produced in collaboration with B. Butoi, S. Levy, T. Munzner, and M.
Teodorescu, (1995 )

·
Seraut-the-dots,
School Arts (2005) Vol 105, November 2005, p. 43. Instructions on
how to carry out a collaborative learning, hands-on art project for 2^{nd}
graders.

·
Family
of Five Math Lesson: the Mathematical Content, joint with Ned Wolff, for West Ed’s Leadership Curriculum
for Mathematics Professional Development project, 2005.

·
Using TIMSS Videos to Improve Learning of Mathematics: A Resource
Guide, Richard Askey and Patsy Wang-Iverson, Editors, 2005. I am acknowledged for contributing to the
resource guide and for reviewing the guide.

·
Quick
Images: the Mathematical Content, joint with Ned Wolff ,
for West Ed’s Leadership Curriculum for Mathematics Professional Development
project, 2006.

·
The
Pit and the Pendulum, Mathematical Commentary for the Interactive Mathematics
Program, joint with Ned Wolff, 2006.

·
Introduction
to the principles of How People Learn and Formative Assessment, a professional
development protocol, MSPGP report, 2007.

·
Differential
Equations and Civic Engagement, in SIGMAA-QL Newsletter, October 2007; in Civic
Matters--A Catalyst for Community Dialogue, a publication of the Civic
Engagement Office at Bryn Mawr College, Issue 2, April 2008.

·
Ordinary
Differential Equations, Mathematical Modeling in Real World Situations.
Donnay’s course curriculum was chosen as a SENCER Model Course for 2008 for its
efforts to improving science learning by supporting
engagement with complex civic issues.
See http://www.sencer.net/Resources/models.cfm .

· The Costa
surface video is displayed (1995-1997) at the Maryland Science Museum as part
of their permanent exhibition on mathematics. Also part of their traveling
exhibit.

· Created a set of color prints
of computer generated pictures of
embedded surfaces with ergodic geodesic
flow. Displayed at :

Artist Market, Norwalk Ct, as part of
Beyond Escher exhibit, November 1998.

MSRI,
Berkeley CA, summer 1999.

Bryn Mawr
College Gallery, fall 2000.

One of these images was used for the cover of the text
Differential Geometry and Topology

by K.Burns and M. Gidea, Chapman & Hall/CRC, 2005.

Co-directed
a summer research program (1996) for Bryn Mawr undergraduates with

D.
Kumar in which the students made interactive Java applets that illustrate the notions of regular and chaotic motion in
dynamical systems (http://serendip.brynmawr.edu/chaos).