Aimee S.A. Johnson

Picture of Professor Johnson

Professor of Mathematics

Department of Mathematics & Statistics
Swarthmore College
Swarthmore, PA 19081

Phone number: 610-328-7357
Fax number: 610-690-6854

Science Center room 143

email: aimee@swarthmore.edu

Courses in Fall 2014:

Math 28 - Honors Linear Algebra ( click here for syllabus)

Math 33 - Basic Several Variable Calculus (click here for syllabus)

Research:

My area of research is in dynamical systems. These originally arose in the study of systems of differential equations and were used to model physical phenomena. One simplification of this is to discretize time, which leads to the study of iterations 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. For instance, ergodic theory studies the statistical and qualitative behavior of group actions on a measure space. It's origins are in the work of Boltzmann in statistical mechanics, where time- and space-distribution averages are equal. Symbolic dynamics studies spaces of infinite sequences of symbols with the dynamics given by the shift operator. It originated with Hadamard's study of geodesics on surfaces of negative curvature and lead to the study of information systems.

Papers:

Directional Recurrence for Infinite Measure Preserving Zd Actions  
[click here for pdf]
Joint work with Ayse Sahin 
Ergodic Theory and Dynamica Systems, to appear

Speedups of Ergodic Group Extensions of Zd Actions
[click here for pdf]
Joint work with David McClendon
Dynamical Systems: An International Journal, to appear

Projectional Entropy in Higher Dimensional Shifts of Finite Type 
[click here for pdf]
Joint work with Steve Kass and Kathleen Madden
Complex Systems, 17 (2007), 243-257

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 Zd 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 Zd 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 Zd
[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

Articles:

The Art of Teaching Mathematics
[click here for pdf]
Joint work with G. Campbell, J. Jacobsen, M.Orrison
MAA Focus 28 (1) (2008)

Pictures:

At conference in honor of Mike Boyle, Spring 2011
At Conference in honor of Mike Boyle: Maryland, Spring 2011

Oxtoby Centennial Conference, Oct 2010
At Oxtoby Centennial Conference, Bryn Mawr College Oct 2010

Expanding Your Horizons Workshop
At an Expanding Your Horizons Workshop

At Pingree Park (Colorado State University) conference in August of 2008
At Pingree Park (Colorado State University) conference in August of 2008

At Dynamics Conference, University of Maryland, Spring 2008At Dynamics Conference, University of Maryland, Spring 2008
At Dynamics Conference, University of Maryland, Spring 2008

At conference in memory of Daniel J. Rudolph, University of Maryland, Spring 2010At conference in memory of Daniel J. Rudolph, University of Maryland, Spring 2010
At conference in memory of Daniel J. Rudolph, University of Maryland, Spring 2010