Department of Mathematics
- NAC 6/274
- Office phone
- (212) 650-5118
I am a professor of mathematics at The City College of New York and also a member of the doctoral faculty at the CUNY Graduate Center. From Fall 2012 to Spring 2016 I served as mathematics department chair at The City College. In addition to teaching, I enjoy mentoring students doing research and independent study projects.
My research is in the areas of dynamical systems and smooth ergodic theory. In particular, I am working on geometric, ergodic- and dimension theoretical aspects of smooth and symbolic dynamical systems. This includes the dynamics on real manifolds (Axiom A, non- uniformly hyperbolic and parabolic systems), shift spaces as well as on one- and higher dimensional complex spaces. Recent research interests include the existence problem of zero-temperature limits, the computability of dynamically defined objects such as rotation sets and their entropies and quantization theory.
- 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, 18 (2016), 1550083, 23 pp.
- (with S. Hayes) Diffeomorphisms with stable manifolds as basin boundaries, Dynamical systems, number theory and applications, 99–112, World Sci. Publ., Hackensack, NJ, 2016.
(with T. Kucherenko) Ground states and zero-temperature measures at the boundary of rotation sets, Ergodic Theory and Dynamical Systems, to appear.