Christian Wolf

Professor

Main Affiliation

Mathematics

Areas of Expertise/Research

  • Ergodic Theory
  • Complex Dynamics
  • Non-Uniformly Hyperbolic Dynamical Systems
  • Thermodynamic Formalism
  • Dimension theory

Building

North Academic Center

Office

6/274

Phone

212-650-5188

Christian

Christian Wolf

Profile

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.

Education

I studied mathematics and physics at the University of Munich in Germany. I then received my PhD at the Technical University of Munich (1999)

Research Interests

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.

Publications

  • P. Javornik, J. Winter and C. Wolf, A horseshoe with a discontinuous entropy function, preprint.

  • M. Burr and C. Wolf, Computability at zero temperature, preprint.

  • C. Wolf, A shift map with a discontinuous entropy function, Discrete and Continuous Dynamical Systems, to appear.

  • C. Wolf and Y. Yang, A topological classification of locally constant potentials via zero-temperature measures, Transactions of the AMS 372 (2019), 3113-3140

  • M. Burr, M. Schmoll and C. Wolf, On the computability of rotation sets and their entropies, Ergodic Theory and Dynamical Systems, Published Online First: 10 August 2018.

  • T. Kucherenko and C. Wolf, Ground states and zero-temperature measures at the boundary of rotation sets, Ergodic Theory and Dynamical Systems 39 (2019), 201-224.

  • S. Hayes and C. Wolf, Diffeomorphisms with stable manifolds as basin boundaries, Dynamical systems, number theory and applications, 99–112, World Sci. Publ., Hackensack, NJ, 2016.

  • T. Kucherenko and C. Wolf, Entropy and rotation sets: A toymodel approach, Communications in Contemporary Mathematics, 18 (2016), 1550083, 23 pp.

  • T. Kucherenko and C. Wolf, Localized pressure and equilibrium states, Journal of Statistical Physics 160 (2015), 1529-1544.

  • T. Kucherenko and C. Wolf, The geometry and entropy of rotation sets, Israel Journal Math. 1999 (2014), 791-829.

  • C. Wolf, Variation of topological pressure and dimension: From polynomials to complex Henon maps, Ergodic Theory Dynamical Systems 34 (2014), 1018-1036.

  • C. Wolf, On barycenter entropy for rational maps, Conformal Dynamics and Hyperbolic Geometry, 233-244, Contemporary Mathematics, 573 AMS, Providence, RI, 2012.

  • K. Gelfert and C. Wolf, On the distribution of periodic orbits. Discrete Continous Dynamical Systems 26 (2010), 949–966.

  • W. Ingle, J.Kaufmann and C. Wolf, Natural invariant measures, divergence points and dimension in one-dimensional holomorphic dynamics. Ergodic Theory Dynamical Systems 29 (2009), 1235–1255.

  • M. Urbanski and C. Wolf, Ergodic theory of parabolic horseshoes , Communications Math. Physics 281 (2008), 711--751.

  • K. Gelfert and C. Wolf, Topological pressure via periodic points, Transactions of the AMS 360 (2008), 545--561.

  • L. Barreira and C. Wolf, Dimension and ergodic decompositions for hyperbolic flows, Discrete and Continuous Dynamical Systems, Series A, 17 (2007), 201-212.

  • K. Gelfert and C. Wolf, Topological pressure for one-dimensional holomorphic dynamical systems, Bulletin of the Polish Academy of Sciences, Mathematics, 55 (2007), 53-62.

  • L. Barreira and C. Wolf, Pointwise dimension and ergodic decompositions, Ergodic Theory and Dynamical Systems, 26 (2006), 653-671.

  • S. Hayes and C. Wolf Dynamics of a one-parameter family of Hénon maps, Dynamical Systems, 21 (2006), 399-407.

  • C. Wolf, Generalized physical and SRB measures for hyperbolic diffeomorphisms, Journal of Statistical Physics 122 (2006), 1111-1138.

  • R. Shafikov and C. Wolf, Stable sets, hyperbolicity and dimension, Discrete and Continuous Dynamical Systems, Series A, 12 (2005), 403-412.

  • M. Urbanski and C. Wolf, SRB measures for Axiom A endomorphisms, Mathematical Research Letters, 11 (2004), 785-797.

  • L. Barreira, L. Radu and C. Wolf, Dimension of measures for suspension flows, Dynamical Systems, 19 (2004), 89-107.

  • 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 C^n. Michigan Mathematical Journal 51 (2003), 631–649.

  • C. Wolf, On measures of maximal and full dimension for polynomial automorphisms of C^2, Transactions of the AMS, 355 (2003), 3227-3239.

  • C. Wolf, Hausdorff and topological dimension for polynomial automorphisms of C^2. Ergodic Theory Dynam. Systems 22 (2002), 1313–1327.

  • C. Wolf, On the box-dimension of an invariant set, Nonlinearity, 14 (2001), 73-79.

  • C. Wolf, Lafuma, R. Masse, M. Morin and A. Kellerer, Neutron RBE for the induction of tumors with high lethality in Sprague-Dawley rats, Radiation Research, 154 (2000), 412-420.

  • C. Wolf, Dimension of Julia sets of polynomial automorphisms of C^2, Michigan Mathematical Journal, 47 (2000), 585-600.