Department of Mathematics
Christian Wolf
 Position

Professor
Graduate Advisor
 cwolf@ccny.cuny.edu
 Office
 NAC 6/274
 Office hours
 Thursday, February 7, 3.30 to 4.30 PM, for other dates contact me by email
 Office phone
 (212) 6505118
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 zerotemperature limits and of measures of maximal dimension, and the computability of dynamically defined objects such as rotation sets, residual entropy and zerotemperature measures.
Research papers
 M. Burr and C. Wolf, Computability at zero temperature, preprint.
 C. Wolf, A shift map with a discontinuous entropy function, preprint.
 C. Wolf and Y. Yang, A topological classification of locally constant potentials via zerotemperature measures, Transactions of the AMS, in press.
 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 zerotemperature measures at the boundary of rotation sets, Ergodic Theory and Dynamical Systems 39 (2019), 201224.
 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), 15291544.
 T. Kucherenko and C. Wolf, The geometry and entropy of rotation sets, Israel Journal Math. 1999 (2014), 791829.
 C. Wolf, Variation of topological pressure and dimension: From polynomials to complex Henon maps, Ergodic Theory Dynamical Systems 34 (2014), 10181036.
 C. Wolf On barycenter entropy for rational maps, Conformal Dynamics and Hyperbolic Geometry, 233244, Contemporary Mathematics, 573 AMS, Providence, RI, 2012.
 (with K. Gelfert) On the distribution of periodic orbits. Discrete Continous Dynamical Systems 26 (2010), no. 3, 949–966.
 W. Ingle, J.Kaufmann and C. Wolf, Natural invariant measures, divergence points and dimension in onedimensional holomorphic dynamics. Ergodic Theory Dynamical Systems 29 (2009), no. 4, 1235–1255.
 M. Urbanski and C. Wolf, Ergodic theory of parabolic horseshoes , Communications Math. Physics 281 (2008), no. 3, 711751.
 K. Gelfert and C. Wolf, Topological pressure via periodic points, Transactions of the AMS 360 (2008), no. 1, 545561.
 L. Barreira and C. Wolf, Dimension and ergodic decompositions for hyperbolic flows, Discrete and Continuous Dynamical Systems, Series A, 17 (2007), 201212.
 K. Gelfert and C. Wolf, Topological pressure for onedimensional holomorphic dynamical systems, Bulletin of the Polish Academy of Sciences, Mathematics, 55 (2007), 5362.
 L. Barreira and C. Wolf, Pointwise dimension and ergodic decompositions, Ergodic Theory and Dynamical Systems, 26 (2006), 653671.
 S. Hayes and C. Wolf Dynamics of a oneparameter family of Hénon maps, Dynamical Systems, 21 (2006), 399407.
 C. Wolf, Generalized physical and SRB measures for hyperbolic diffeomorphisms, Journal of Statistical Physics 122 (2006), 11111138.
 R. Shafikov and C. Wolf, Stable sets, hyperbolicity and dimension, Discrete and Continuous Dynamical Systems, Series A, 12 (2005), 403412.
 M. Urbanski and C. Wolf, SRB measures for Axiom A endomorphisms, Mathematical Research Letters, 11 (2004), 785797.
 L. Barreira, L. Radu and C. Wolf, Dimension of measures for suspension flows, Dynamical Systems, 19 (2004), 89107.
 L. Barreira and C. Wolf, Measures of maximal dimension for hyperbolic diffeomorphisms, Communications Math. Physics 239 (2003), 93113.
 R. Shafikov and C. Wolf, Filtrations, hyperbolicity, and dimension for polynomial automorphisms of C^n. Michigan Mathematical Journal 51 (2003), no. 3, 631–649.
 C. Wolf, On measures of maximal and full dimension for polynomial automorphisms of C^2, Transactions of the AMS, 355 (2003), 32273239.
 C. Wolf, Hausdorff and topological dimension for polynomial automorphisms of C^2. Ergodic Theory Dynam. Systems 22 (2002), no. 4, 1313–1327.
 C. Wolf, On the boxdimension of an invariant set, Nonlinearity, 14 (2001), 7379.
 C. Wolf, Lafuma, R. Masse, M. Morin and A. Kellerer, Neutron RBE for the induction of tumors with high lethality in SpragueDawley rats, Radiation Research, 154 (2000), 412420.
 C. Wolf, Dimension of Julia sets of polynomial automorphisms of C^2, Michigan Mathematical Journal, 47 (2000), 585600.
 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, upcoming.
 A topological classification of locally constant potentials via zerotemperature 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 zerotemperature measures,} Algorithmic Questions in Dynamical Systems Workshop, Institut de Mathematiques de Toulouse, Toulouse France, March 2018.
 Zerotemperature measures, entropy and rotation sets, Spring Topology and Dynamical Systems Conference, Auburn, AL, March 2018.
 Zerotemperature 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 zerotemperature 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.
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