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# Bruce Kitchens

Professor, Mathematical Sciences

## Teaching Assignments

## Current Research

Prof. Kitchens primary interests are in dynamical systems and ergodic theory. His papers have been in the areas of symbolic dynamics, algebraic dynamics, piecewise dynamics, entropy theory, topological dynamics and game theory. He has also done work concerning information theory in the areas of channel coding, convolutional codes and printing algorithms. He is currently working on problems in game theory, algebraic dynamics and the connections between complex dynamics and symbolic dynamics.

Dr. Kitchens's web page

## Select Publications

### Books

- B. Kitchens and S.Tuncel, Finitary Measures for Subshifts of Finite Type and Sofic Systems. Memoirs of the American Mathematical Society, No. 338,1985, 68 pages.
- B. Kitchens, Symbolic Dynamics: One-sided, Two-sided and Countable State Markov Shifts, Springer, 1998, 252 pages.

**Research Articles**

- B. Kitchens, An Invariant for Continuous Factors of Markov Shifts. Proceedings of the American Mathematical Society, 83 (1981), 825-828.
- R.L. Adler, B. Kitchens and B.H. Marcus, Finite Group Actions on Shifts of Finite Type, Ergodic Theory and Dynamical Systems, 5 (1985), 1-25.
- B. Kitchens, Expansive Dynamics on Zero Dimensional Groups. Ergodic Theory and Dynamical Systems, 7 (1987), 249-261.
- B. Kitchens and K. Schmidt, Automorphisms of Compact Groups, Ergodic Theory and Dynamical Systems, 9 (1989), 691-735.
- M. Boyle, J. Franks and B. Kitchens , Automorphisms of One-Sided Subshifts of Finite Type, Ergodic Theory and Dynamical Systems 10 (1990), 421-449.
- J. Ashley, B. Kitchens and M. Stafford, Boundaries of Markov partitions, Transactions of the American Mathematical Society. AMS, Vol. 333, No. 1 (1992), 177-20.
- B. Kitchens and K. Schmidt, Mixing sets and relative entropies for higher dimensional Markov shifts, Ergodic Theory and Dynamical Systems 13, (1993), 703-735.
- M. Handel and B. Kitchens, Metrics and entropy for noncompact spaces, Israel Journal of Mathematics, 91 (1995), 253-271.
- B. Kitchens and K. Schmidt, Isomorphism Rigidity of Simple Algebraic Z
^{d}-actions, Inventiones Mathematicae, 142 (2000), 559-577. - R. Adler, B. Kitchens and C. Tresser, Dynamics of Piecewise Affine Maps of the Torus, Ergodic Theory and Dynamical Systems 21, (2001), 959-999.
- R.L. Adler, B. Kitchens, M. Martens, C. Pugh M. Shub and C.Tresser Convex Dynamics and Applications, Ergodic Theory and Dynamical Systems, Vol. 25, No. 2 (2005), 321-352.
- R. Becker, S. Chakrabarti, W. Geller B. Kitchens and M. Misiurewicz, Dynamics of the Nash Map in the Game of Matching Pennies, Journal of Difference Equations and Applications, Vol. 13 (2007), 223-235.

**Recent Articles**

- B. Kitchens, Symbolic Dynamics of Tree Maps, Journal of Difference Equations and Applications, 15 (2009), 71-76.
- R. Becker, S. Chakrabarti, W. Geller, B. Kitchens, and M. Misiurewicz, Hyperbolic Dynamics in Nash Maps, Discrete Dynamics and Difference Equations: Proceedings of the Twelfth International Conference on Difference Equations and Applications; editors: Saber Elaydi, Henrique Oliveira, Jose Manuel Ferreira and Joao Alves; World Scientific, Singapore, 2010.
- R. Becker, S. Chakrabarti, W. Geller, B. Kitchens, and M. Misiurewicz, The Dynamics of 2 by 2 Games, Dynamics, Games and Science II, Springer Proceedings in Mathematics, 2011, Volume 2, 549-565.
- W. Geller, B. Kitchens and M. Misiurewicz, Microdynamics, Discrete and Continuous Dynamical Systems, Vol. 27, No. 3 (2010), 1007 -1024.
- B. Kitchens and M. Misiurewicz, Omega-limit sets for spiral maps, Discrete and Continuous Dynamical Systems, Vol. 27, No. 2 (2010), 787 - 798.
- B. Kitchens and M. Misiurrewicz , Omega-limit sets for spiral maps, Discrete and Continuous Dynamical Systems, Vol. 27, No. 2 (2010), 787 - 798.
- B. Kitchens, W. Geller, M.Misiurewicz and M. Rams, A Spectral Radius Estimate and Entropy of Hypercubes, International Journal of Bifurcation and Chaos, Vol. 22, No. 4 (2012)
- B. Kitchens, Intrinsically nonmixing sets and dynamical rigidity, preprint.

### Expository Articles

- M. Grayson, B. Kitchens and G. Zettler, Visualizing toral automorphisms, Mathematical Intelligencer, Vol. 15, No. 4, Winter 1993, 63-66.
- B. Kitchens, Symbolic Dynamics, Group Automorphisms and Markov Partitions, Real and complex dynamics,
*(ed. B. Branner and P. Hjorth),*Burkhauser, 1995, 133-164. - B. Kitchens, The Dynamics of Group Automorphisms, Annals of Numerical Mathematics, Volume in honor of T. Rivlin, 4 (1997), 369-391.
- B. Kitchens, Introduction to Pricing Derivative Securities, IBM Lecture Notes No. 237, 1998, 25 pages.
- B. Kitchens, Dynamics of Z
^{d}-actions on Markov Subgroups, Topics in Symbolic Dynamics and Applications (ed. F. Blanchard, A. Maass and A. Nogueira), London Mathematical Society Lecture Series, Cambridge, 2000, 89-118. - B. Kitchens, Review of Computational Ergodic Theory, by Geon Ho Cho, Bulletin of the American Mathematical Society, Vol. 45, No. 1, 2007, 147-155.

- phone: (317) 274-6933
- office: LD 270H
- e-mail: bkitchens@math.iupui.edu

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