Department of Mathematics
I studied mathematics and physics at the University of Munich in Germany. After my PhD at the Technical University of Munich (1999), I taught at Indiana University, Bloomington from 1999 through 2001, and spend the year of 2002 at the Technical University of Lisbon. In the Spring of 2003 I joined Wichita State University in Kansas where I stayed until Spring 2010. Finally, in Fall of 2010, I arrived at the City College.
My research is in the area of dynamical systems, essentially the mathematics
of systems which change under evolution of time. In particular, I am working on
geometric, ergodic- and dimension theoretical aspects of smooth dynamical
systems. This includes the dynamics on real manifolds (Axiom A, non-
uniformly hyperbolic and parabolic systems) as well as on one- and higher dimensional
complex spaces. In my work I combine tools from several areas of
mathematics such as ergodic theory, real and complex analysis, geometry, dimension
theory and the thermodynamic formalism.
- Hausdorff and topological dimension for polynomial automorphisms of C^2. Ergodic Theory Dynam. Systems 22 (2002), no. 4, 1313–1327.
- (with L. Barreira) Measures of maximal dimension for hyperbolic diffeomorphisms, Communications Math. Physics 239 (2003), 93-113.
- (with R. Shafikov) Filtrations, hyperbolicity, and dimension for polynomial automorphisms of C^n. Michigan Math. J. 51 (2003), no. 3, 631–649.
- Generalized physical and SRB measures for hyperbolic diffeomorphisms, Journal of Statistical Physics 122 (2006), 1111-1138.
- (with K. Gelfert) Topological pressure via periodic points, Trans. Amer. Math. Soc. 360 (2008), no. 1, 545--561.
- (with M. Urbanski) Ergodic theory of parabolic horseshoes , Communications Math. Physics 281 (2008), no. 3, 711--751.
- (with W. Ingle and J.Kaufmann) Natural invariant measures, divergence points and dimension in one-dimensional holomorphic dynamics. Ergodic Theory Dynam. Systems 29 (2009), no. 4, 1235–1255.
- (with K. Gelfert) On the distribution of periodic orbits. Discrete Contin. Dyn. Syst. 26 (2010), no. 3, 949–966.
- Variation of topological pressure and dimension: From polynomials to complex Henon maps, Ergodic Theory Dynam. Systems 34 (2014), 1018-1036.
- (with T. Kucherenko) The geometry and entropy of rotation sets,
Israel Journal Math. 1999 (2014), 791-829.
- (with T. Kucherenko) Localized pressure and equilibrium states, Journal of Statistical Physics 160 (2015), 1529-1544.
- (with T. Kucherenko) Entropy and rotation sets: A toymodel approach, Communications in Contemporary Mathematics, to appear.
- (with S. Hayes) Diffeomorphisms with stable manifolds as basin boundaries, World Scientific, to appear.