Christian Wolf

Christian Wolf, Associate Professor

Dynamical Systems; PhD, Technical University of Munich, 1999

Contact

Awards

NSF-EPSCOR First Award, 2004

PhD Students

Raja Balakrishnan (current)

Research

Dr. Wolf's research interests lie in the areas dynamical systems, smooth ergodic theory and complex dynamics in several variables. In particular, he is working on ergodic and dimension-theoretical aspects of real and complex dynamical systems and their relations to geometric properties of the corresponding invariant sets and measures. Recently, he has become interested in generalizations of natural invariant measures (SRB measures, physical measures, measures of maximal dimension, etc.) and has analyzed these measures for several hyperbolic as well as parabolic systems. Another aspect of his work concerns the connection between the topological pressure and geometric as well dynamical properties of the underlying dynamical system in particular in the case of non-uniformly hyperbolic dynamics. In his work he combines tools from several different areas of mathematics such as ergodic theory, complex analysis, real and complex dynamics and the thermodynamic formalism.

Selected Publications

  • C. Wolf, On measures of maximal and full dimension for polynomial automorphisms of C2, Trans. Amer. Math. Soc. 355 (2003), 3227-3239.
  • L. Barreira and C. Wolf, Measures of maximal dimension for hyperbolic diffeomorphisms, Communications Math. Physics 239 (2003), 93-113.
  • R. Shafikov and C. Wolf, Filtrations, hyperbolicity and dimension for polynomial automorphisms of Cn, Michigan Math. J. 51 (2003) no. 3, 631-649.
  • M. Urbanski and C. Wolf, SRB measures for Axiom A endomorphisms, Mathematical Research Letters, Mathematical Research Letters 11 (2004), no. 5-6, 785-797.
  • C. Wolf, Generalized physical and SRB measures for hyperbolic diffeomorphisms, Journal of Statistical Physics, Vol. 122, No. 6, March 2006, 1111-1138.
  • M. Urbanski and C. Wolf, Ergodic Theory of parabolic horseshoes, preprint.