Division of Science

Programs

General

External

Contact

Department of Mathematics
The City College of New York
160 Convent Avenue
New York, NY 10031

Phone: (212) 650-5346
Fax: (212) 650-6294
math@ccny.cuny.edu

Christian Wolf

Position
Professor
Graduate Advisor
Email
cwolf@ccny.cuny.edu
Office
NAC 6/274
Office hours
Tuesday, 2.00 to 3.30 PM, for other dates contact me by email.
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 and of measures of maximal dimension, and the computability of dynamically defined objects such as rotation sets, residual entropy and zero-temperature measures.


Research papers

  • 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 40 (2020), 319-329.

  • 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.

  • Research Presentations


  • Computability of Rotation sets and their entropies, Analysis Seminar, Virginia Tech, November 2019.

  • Geometry and computability at zero temperature, Ergodic Theory and related Fields Conference, Bucharest, Romania, October 2019.

  • Computability of Thermodynamic invariants on shift spaces beyond SFTS, Millican Colloquium, University of North Texas, September 2019.

  • Geometry and computability at zero temperature, Dynamics of (Semi-)Group Actions Conference, Lodz, Poland, July 2019.

  • Geometry and computability at zero temperature, 8th Visegrad Conference on Dynamical Systems, Budapest, Hungary, June 2019.

  • Pressure and dimension: From polynomials to hyperbolic and parabolic Henon maps, Special Session on Constructive Aspects of Complex Analysis, AMS Sectional Meeting, Honolulu, HI, March 2019.

  • A topological classification of locally constant potentials via zero-temperature measures, Complex Analysis and Dynamics Seminar, CUNY Graduate Center, New York, NY, January 2019.

  • Computability at zero temperature, Thirteenth International Conference on Computability, Complexity and Randomness, Santiago, Chile, December 2018.

  • Computability at zero temperature, Special Session on Statistical and Geometrical Properties of Dynamical Systems, AMS Sectional Meeting, San Francisco, CA, October 2018.

  • Computability at zero temperature, Complex Analysis and Dynamics Seminar, CUNY Graduate Center, New York, NY, October 2018.

  • Regularity of the localized entropy function, Complex Analysis and Dynamics Seminar, CUNY Graduate Center, New York, NY, April, 2018.

  • Computability of thermodynamic invariants: pressure, entropy and zero-temperature measures, Algorithmic Questions in Dynamical Systems Workshop, Institut de Mathematiques de Toulouse, Toulouse France, March 2018.

  • Zero-temperature measures, entropy and rotation sets, Spring Topology and Dynamical Systems Conference, Auburn, AL, March 2018.

  • Zero-temperature measures, entropy and rotation sets, Dynamical Systems Seminar, University of Toronto, Canada, January 2018.

  • Measures of maximal dimension for surface diffeomorphisms: Old and New, Dynamical Systems Seminar, CUNY Graduate Center, NY, November 2017.

  • On the computability of rotation sets and their entropies, Special Session on Fractal Geometry, Dynamical Systems, and their Applications, AMS Sectional Meeting, Orlando, FL, September 2017.

  • On the computability of rotation sets and their entropies, Special Session on Dynamics, Geometry and Number Theory, AMS Sectional Meeting, Denton, TX, September 2017.

  • On computability of rotation sets and their entropy, Dynamical Systems Seminar, Stonybrook University, NY, May 2017.

  • On computability of rotation sets and their entropy, Analysis Seminar, Clemson University, SC, April 2017.

  • Ground states and zero-temperature measures at the boundary of rotation sets, Carolina Dynamics Symposium, University of North Carolina, Charlotte, NC, April 2017.

  • Entropy of Rotation Classes, Dynamical Systems Session, 51st Spring Topology and Dynamical Systems Conference, Jersey City, NJ, March 2017.

  • Geometric properties of ground state rotation vectors, Physics Colloquium, The City College of New York, New York, NY, February 2017.

  • Are rotation sets and localized entropies computable?, Ergodic Theory and Dynamical Systems Session, Joint Mathematics Meeting, Atlanta, GA, January 2017.

  • Ground states, mutual ergodic optimization and rotation sets, Dynamical Methods in Open Quantum Systems Workshop, Goettingen, Germany, November 2016.

  • Ground states and mutual ergodic optimization, Complex Analysis and Dynamics Seminar, CUNY Graduate Center, NY, November 2016.

  • Ground states at the boundary of rotation Sets, Lecture Series in Mathematical Sciences, Wichita State University, KS, September 2016.

  • On zero temperature measures, Special Session on Invariant Measures of Dynamical Systems, AMS Sectional Meeting, Athens, GA, April 2016.

  • Localized equilibrium states and rotation sets, 49th Spring Topology and Dynamics Conference, Bowling Green, OH, May 2015.

  • Localized pressure and equilibrium states, Logic, Dynamics and their Interactions Conference, Denton, TX, June 2014.

  • Localized pressure and equilibrium states, Dynamical Systems Seminar, Penn State University, State College, PA, April 2014.



  • My research is supported by a grant from the Simons Foundation (#637594 to Christian Wolf)

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