# Christian Wolf

- Position
- Professor
- cwolf@ccny.cuny.edu
- Office
- MR 330
- Office hours
- By appointment.
- Office phone
- (212) 650-5173
- M. Burr and C. Wolf, Computability in dynamical systems, preprint.
- M. Burr, S. Das, C. Wolf and Y. Yang, Computability of topological pressure on compact shift spaces beyond finite type, Nonlinearity 35, 2022, 4250-4282.
- L. Demetrius and C. Wolf, Directionality Theory and the Second Law of Thermodynamics, Physica A 598, 2022, 127325.
- Y. M. He and C. Wolf, Entropy spectrum of rotation classes, Journal of Mathematical Analysis and Applications 508, 2022, 125851.
- T. Kucherenko, A. Quas and C. Wolf, Multiple phase transitions on compact symbolic systems, Advances in Mathematics 385, 2021, 107768.
- P. Javornik, J. Winter and C. Wolf, A horseshoe with a discontinuous entropy function, Journal of Mathematical Analysis and Applications 496, 2021, 124811.
- M. Burr and C. Wolf, Computability at zero temperature, Nonlinearity 33, 2020, 6157-6175.
- M. Burr, M. Schmoll and C. Wolf, On the computability of rotation sets and their entropies, Ergodic Theory and Dynamical Systems 40 (2020), 367-401.
- 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.
- 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 Continuous 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.
- Computability in dynamical systems, Geometry of Deterministic and Random Fractals Conference, Technical University of Budapest, June 2022.
- Computability in dynamical systems, AMS Spring Western Sectional Meeting (Virtual), Special Session on Fractal Geometry and Dynamical Systems, May 2022.
- Computability of topological pressure on compact shift spaces beyond finite type, Ergodic Theory Seminar, Ohio State University, September 2021.
- Geometry and computability of zero-temperature measures, The 9th Visegrad Conference Dynamical Systems, Prague, June 2021.
- Computability of topological pressure on compact shift spaces beyond finite type, Joint Mathematics Meeting, AMS Special Session on Quantization for Probability Distributions and Dynamical Systems, January 2021.
- Computability of topological pressure on compact shift spaces beyond finite type, Dynamical Systems Seminar, Jagiellonian University in Krakow, December 2020.
- Computability of topological pressure on compact shift spaces beyond finite type, Dynamics and Computations Seminar, Uppsala University, November 2020.
- Computability of topological pressure on compact shift spaces beyond finite type, Dyn-Sys-zoominar , University of Porto, November 2020.
- 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.

I currently serve as the Executive Officer of the Ph.D. program in Mathematics at the CUNY Graduate Center. Please contact me at cwolf@gc.cuny.edu for all Graduate Center related inquiries.

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 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.

### Teaching

- This term I am teaching MATH 83900: Symbolic Dynamical Systems
at the CUNY Graduate Center.

### Research

- 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, 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).