Michal Misiurewicz

Research

My major research activities are in Dynamical Systems and Ergodic Theory. Those areas of Mathematics are about the evolution of various systems in time, from the differential, topological and statistical points of view. Main objects of interest in my research are one-dimensional systems, entropy, periodic orbits and connections with other parts of Mathematics and other sciences, including applications of Dynamical Systems.

One-dimensional systems are especially interesting, since they display many features of more general systems, while it is possible to apply special tools for their investigation. My proofs of existence of an absolutely continuous measure (which means that the system is chaotic, but can be successfully studied from the statistical points of view) were acknowledged in names like “Misiurewicz maps” in real dynamics and “Misiurewicz points” in complex dynamics.

Another interesting aspect of one-dimensional dynamics studied by me is relation between periodic orbits of various periods and relation between those orbits and the measure of chaos, topological entropy. This constitutes a new area of Dynamical Systems, Combinatorial Dynamics. A book I wrote with my collaborators from Barcelona, Spain, is an important resource in this area.

Following current trends, I study random dynamical systems, including quasiperiodically forced ones, and connections with other branches of Mathematics, for instance Braid Theory and Game Theory. I also apply my expertise to systems arising in various sciences, like Economics and Mathematical Biology. In particular, together with my colleagues from the Department of Mathematical Sciences and economists from this campus and IU Bloomington, I study models of so called Nash maps, coming from Economics.

Education

• 1971  MS, University of Warsaw, Warsaw, Poland
• 1974  PhD, University of Warsaw, Warsaw, Poland

Publications & Professional Activity

Book:

Ll Alseda, J Llibre and M Misiurewicz (1993; Second Edition 2000) Combinatorial dynamics and entropy in dimension one, World Scientific.

Selected Papers:

• M Misiurewicz (1976) Topological conditional entropy, Studia Math. 55, 175--200.

• M Misiurewicz (1976) A short proof of the variational principle for a Z^N_+ action on a compact space, Asterisque 40, 147--157.

• M Misiurewicz and F Przytycki (1977) Topological entropy and degree of smooth mappings, Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys. 25, 573--574.

• M Misiurewicz and W Szlenk (1980) Entropy of piecewise monotone mappings, Studia Math. 67, 45--63.

• L Block, J Guckenheimer, M Misiurewicz and LS Young (1980) Periodic points and topological entropy of one dimensional maps in: Global Theory of Dynamical Systems, Lecture Notes in Math. 819, Springer, Berlin, 18--34.

• M Misiurewicz (1981) Absolutely continuous measures for certain maps of an interval, Publ. Math. IHES 53, 17--51.

• M Misiurewicz and K Ziemian (1989) Rotation sets for maps of tori, J. London Math. Soc. (2) 40, 490--506.

• V Bergelson, M Misiurewicz and S Senti (2006) Affine actions of a free semigroup on the real line, Ergod. Th. & Dynam. Sys. 26, 1285--1305.

• M Misiurewicz and A Rodrigues (2007) Double standard maps, Commun. Math. Phys. 273, 37--65.

List of publications

Awards

• Aulback Prize, International Society of Difference Equations (2013) 
• American Mathematical Society Fellow (2012)
• Trustees Teaching Award, IUPUI (2010)
• Sierpinski Medal, Polish Mathematical Society and University of Warsaw (2003)
• Mazur Prize, Polish Mathmatical Society (1988)
• Award for research, Scientific Secretary of the Polish Academy of Sciences (1988)
• Award of Second Degree for research, Minister of Science, Higher Education and Technology of Poland (1984)
• Award of Third Degree for research, Minister of Science, Higher Education and Technology of Poland (1981)
• Mazurkiewicz Prize, Polish Mathematical Society (1980)
• Award for research, Division of Mathematical-Physical, Chemical and Geological-Geographical Sciences of the Polish Academy of Sciences (1977)
• Award for Young Mathematicians, Polish Mathematical Society (1977)
• Award of Third Degree for the PhD Thesis, Minister of Science, Higher Education and Technology of Poland (1975)