# Karen Brucks

## Associate Professor

(Associate Dean, Natural Sciences)

**Office:** NWQ B 5488

**Phone:** (414) 229-2925

**E-mail:** kmbrucks@uwm.edu

**Web:** http://pantherfile.uwm.edu/kmbrucks/www

Curriculum Vitae

### Educational Degrees

Ph.D. Mathematics, North Texas State University, 1988

M.A. Mathematics, North Texas State University, 1982

B.A. Mathematics, University of Arizona, 1980

### Research Interests

- Dynamical Systems
- Topological, symbolic, and measurable dynamics

### Selected Service, Projects, and Publications

Alvin, Lori, and Brucks, Karen M. “Adding machines, kneading maps, and endpoints.”

*Topology and its Applications*158.3 (2011): 542-550.Alvin, Lori, and Brucks, Karen M. “Adding machines, endpoints, and inverse limit spaces.”

*Fundamenta Mathematicae*209.1 (2010): 81-93.Brucks, Karen M., and Bruin, Henk. “Topics from one-dimensional dynamics.” 62. Cambridge University Press. (2004) .

Brucks, Karen M., Ringland, John, and Tresser, Charles. “An embedding of the Farey web in the parameter space of simple families of circle maps.”

*Physica D. Nonlinear Phenomena*161.3-4 (2002): 142-162.Brucks, Karen M., and Buczolich, Zoltán. “Universality in inverse limit spaces of the logistic family occurs with positive measure.”

*Atti del Seminario Matematico e Fisico dell'Università di Modena*48.2 (2000): 335-353.Brucks, Karen M., and Buczolich, Zoltán. “Trajectory of the turning point is dense for a co-σ-porous set of tent maps.”

*Fundamenta Mathematicae*165.2 (2000): 95-123.Brucks, Karen M., and Bruin, Henk. “Subcontinua of inverse limit spaces of unimodal maps.”

*Fundamenta Mathematicae*160.3 (1999): 219-246.Brucks, Karen M., Galeeva, R., Mumbrú, P., Rockmore, D., and Tresser, C. “On the ∗-product in kneading theory.”

*Fundamenta Mathematicae*152.3 (1997): 189-209.Brucks, Karen M., and Misiurewicz, Michal. “The trajectory of the turning point is dense for almost all tent maps.”

*Ergodic Theory and Dynamical Systems*16.6 (1996): 1173-1183.Barge, Marcy, Brucks, Karen M., and Diamond, Beverly. “Self-similarity in inverse limit spaces of the tent family.”

*Proceedings of the American Mathematical Society*124.11 (1996): 3563-3570.Brucks, Karen M., and Tresser, C. “A Farey tree organization of locking regions for simple circle maps.”

*Proceedings of the American Mathematical Society*124.2 (1996): 637-647.Brucks, Karen M., and Diamond, Beverly. “A symbolic representation of inverse limit spaces for a class of unimodal maps.”

*Continua, Dekker*170. (1995): 207-226.Brucks, Karen M., Otero-Espinar, Maria Victoria, and Tresser, Charles. “Homeomorphic restrictions of smooth endomorphisms of an interval.”

*Ergodic Theory and Dynamical Systems*12.3 (1992): 429-439.Brucks, Karen M., Misiurewicz, M., and Tresser, C. “Monotonicity properties of the family of trapezoidal maps.”

*Communications in Mathematical Physics*137.1 (1991): 1-12.Brucks, Karen M., and Diamond, B. “Monotonicity of auto-expansions. Nonlinear science: the next decade.”

*Physica D. Nonlinear Phenomena*51.1-3 (1991): 39-42.Brucks, Karen M., Diamond, B., Otero-Espinar, M. V., and Tresser, C. “Dense orbits of critical points for the tent map.”

*Continuum theory and dynamical systems, Amer. Math. Soc.*117. (1991): 57-61.Brucks, Karen M. “Uniqueness of aperiodic kneading sequences.”

*Proceedings of the American Mathematical Society*107.1 (1989): 223-229.Brucks, Karen M. “Hausdorff dimension and measure of basin boundaries.”

*Advances in Mathematics*78.2 (1989): 168-191.Brucks, Karen M. “MSS sequences, colorings of necklaces, and periodic points of f(z)=z^2−2.”

*Advances in Applied Mathematics*8.4 (1987): 434-445.