Dynamical Systems:

Dynamical Systems originally arose in the study of systems of differential equations used to model physical phenomena. One simplification of this is to discretize time, which leads to the study of iterates of a single transformation acting on a space. One can then study the global behavior of the system and the probabilistic happenings of this space. Different assumptions can be placed on the space and the map, and these lead to different areas of study in dynamical systems: topological, symbolic, measurable, differential, or hyperbolic. I have worked in the first three of these.

Papers:

Projectional Entropy in Higher Dimensional Shifts of Finite Type
joint work with Steve Kass and Kathleen Madden
Complex Systems (to appear)

The Relative Growth of Information in Two-Dimensional Partitions [click here for pdf]
joint work with Karma Dajani and Martijn de Vries
Real Analysis Exchange, 31 No 2 (2005/2006)

Factoring Higher Dimensional Shifts of Finite Type onto the Full Shift [click here for pdf]
joint work with Kathleen Madden
Ergodic Theory and Dynamical Systems, 25 (2005)

The Symbolic Dynamics of Multidimensional Tilings Systems
[click here for pdf]
joint work with Ethan Coven, Natasa Jonaska, and Kathleen Madden
Ergodic Theory and Dynamical Systems, 23 (2003), 447 - 460

Renewal Systems, Sharp Eyed Snakes, and Shifts of Finite Type
[click here for pdf]
joint work with Kathleen Madden
American Mathematical Monthly 109 No 3 (2002), 258 - 272

Even Kakutani Equivalence and the Loose Block Independence Property for Positive Entropy Z^d Actions [click here for pdf]
joint work with Ayse Sahin
Illinois Journal of Mathematics, 45 No 2 (2001), 495 - 516

Isometric Extensions of Zero Entropy Z^d Loosely Bernoulli Transformations [click here for pdf]
joint work with Ayse A. Sahin
Transactions of the American Mathematical Society, 352 No 3 (2000), 1329-1343

Recurrent Sequences and IP Sets [click here for pdf]
joint work with Kamel Haddad
Topology and its Applications, 98 Vol. 1-3 (1999), 203 - 210

The Decomposition Theorem for Two-DimensionalSubshifts of Finite Type [click here for pdf]
joint work with Kathleen Madden
Proceedings of the AMS, 127 N0. 5 (1999), 1533 - 1543

Finite Rank Z^d Actions and the Loosely Bernoulli Property
[click here for pdf]
joint work with Ayse A. Sahin
New York Journal of Mathematics, 3A (1998), 125 - 134

Rank One and Loosely Bernoulli in Z^d [click here for pdf]
joint work with Ayse A. Sahin
Ergodic Theory and Dynamical Systems, 18 (1998), 1159 - 1172

IP Cluster Points, Idempotents, and Recurrent Sequences
[click here for pdf]
joint work with Kamel N. Haddad
Topology Proceedings, 22 (1997), 213 - 226

Putting the Pieces Together: Understanding Robinson's Nonperiodic Tilings [click here for pdf]
joint work with Kathleen Madden
The College Mathematics Journal, 28 No. 3 (1997), 172 - 181

Auslander Systems [click here for pdf]
joint work with Kamel N. Haddad
Proceedings of the AMS, 125 No. 7 (1997), 2161 - 2179

A Dynamical System with a Z² Centralizer [click here for pdf]
joint work with Kyewon Koh Park
Journal of Mathematical Analysis and Applications, 210 (1997), 337 - 359

Convergence under xp of xq Invariant Measures on the Circle
[click here for pdf]
joint work with Daniel J. Rudolph
Advances in Mathematics, 115 (1995), 117 - 140

Commuting Endomorphisms of the Circle [click here for pdf]
joint work with Daniel J. Rudolph
Ergodic Theory and Dynamical Systems 12 (1992), 743 - 748

Measures on the Circle Invariant under Multiplication by a Nonlacunary Subsemigroup of the Integers [click here for pdf]
Israel Journal of Mathematics 77 (1992), 211 - 240