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.

 

 

Educational Materials

 

·      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 2nd 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 .

 

 

Exhibits

 

·      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.

 

 

Web Materials

 

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).