Christian Wolf

Professor

Main Affiliation

Mathematics

Areas of Expertise/Research

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

Building

Marshak Science Building

Office

MR 330

Phone

212-650-5173

Website

Christian

Christian Wolf

Profile

I am a professor of mathematics at T¾ÅÉ«ÊÓÆµ and also a member of the doctoral faculty at the CUNY Graduate Center. From 2012 to 2016 and 2021 to 2022 I served as mathematics department chair at The City College. In addition to teaching, I enjoy mentoring students doing research and independent study projects.

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 ergodic theory and dynamical systems. 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 and of measures of maximal dimension, the computability of dynamically defined objects such as rotation sets, residual entropy and zero-temperature measures, and the application of the thermodynamic formalism to evolutionary biology. My research is supported by a Collaboration Grant for Mathematicians from the Simons Foundation (#637594 to Christian Wolf).

Publications

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

  • M. Burr and C. Wolf, , preprint.

  • C. Wolf, , Discrete and Continuous Dynamical Systems, to appear.

  • C. Wolf and Y. Yang, , Transactions of the AMS 372 (2019), 3113-3140

  • M. Burr, M. Schmoll and C. Wolf, , 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.