Ning Zhong

Ning Zhong , Ph.D. University of Wisconsin at Madison, 1991



French Hall


A&S Mathematical Sciences - 0025


PhD: University of Wisconsin at Madison 1991

Research and Practice Interests

Theory of real computing; in particular, computability and complexity in
analysis and physics. 

Abbreviated Publications

Peer Reviewed Publications

(Selected publications. If you have access to MathSciNet you can see other publications.)

Computing the exact number of periodic orbits for planar flows (with Daniel S. Graca),  Transactions of the American Mathematical Society
published electronically: May 26, 2022, 47 pages. DOI: 

Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines, Computability - The Journal of the Association Computability in Europe,  Vol 12, No 2, 117 - 144, 2023

Computability of the Solutions to Navier-Stokes Equations via Effective Approximation (with S. Sun and M. Ziegler), Lecture Notes in Comput. Sci. book series Complexity and Approximation edited by Dingzhu Du and Jie Wang (2020), 80 -- 112, Springer.

Computability of Differential Equations (with D. S. Grac}a), chapter 3 in Handbook of Computability and Complexity in Analysis edited by Vasco Brattka and Peter Hertling (2021), 71 - 99, Springer.

The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable,  Theoret. Comput. Sci.  Vol 895, 2021, 48 - 54.

 Computing geometric Lorenz attractors with arbitrary precision ( with D. S. Graca and C. Rojas),  Trans. Amer. Math. Soc.  370(2018), no. 4, 2955–2970

On sharpness of the local Kato-smoothing property for dispersive wave equations (with S.M. Sun, E. Trelat, and B.Y. Zhang),  Proc. Amer. Math. Soc. 145(2017), 653 – 664

An analytic System with a Computable Hyperbolic Sink Whose Basin of Attraction is Non-Computable (with Daniel Graca), Theory Comput. Syst. Volume 57, Issue 2 (2015), 478 -- 520

Computability aspects for 1st-order partial differential equations via characteristics (with S. Sun), Theoret. Comput. Sci.Volume 583, Issue C (2015), 27 -- 39

On Computability of Navier-Stokes’ Equation (with S. Sun and M. Ziegler),  Lecture Notes in Comput. Sci., Volume 9136 (2015), 334-342 

On Effective Convergence of Numerical Solutions for Differential Equations (with S. Sun),  ACM Trans. Comput. Theory, Vol. 6, No. 1 (2014), 55 -- 80

A Tribute to Marian Boykan Pour-El (1928 -- 2009) (with I. Pour-El),   J. Logic Comput. 25(2015), no. 4, 1133 - 1140 

Computability and computational complexity of the evolution of nonlinear dynamical systems (with O. Bournez, D. S. Graca, and A. Pouly),  Lecture Notes in Comput. Sci.,, volume 7921 (2013), 12 – 21

Computability, Noncomputability, and Hyperbolic Systems (with D.S. Graca and J. Buescu),  Appl. Math. Comput. 219 (2012), no. 6, 3039 –- 3054

The connection between computability of a nonlinear problem and its linearization: The Hartman-Grobman theorem revisited (with D.S.Graca and H.S.Dumas),  Theoret. Comput. Sci.  457 (2012), 101 -- 110

Computability and Dynamical Systems (with J. Buescu and D.S. Graca), Dynamics, Games, and Science I, Mauricio Matos Peixoto, Alberto Adrego Pinto, David A. Rand (Eds.), Springer Proc. Math., Vol. 1 (2011), 169 - 182

Computability in planar dynamical systems (with D. S. Graca), Nat. Comput., Volume 10, Issue 4 (2011), 1295 -- 1312.

Computational unsolvability of domains of attraction of nonlinear systems,  Proc. Amer. Math. Soc. 137 (2009), 2773-2783.

Topological complexity of blowup problems (with R. Rettinger & K. Weihrauch), J.UCS 15 (1009), no. 6, 1301-1316

Computability, noncomputability and undecidability of maximal intervals of IVPs (with D.S. Graca & J. Buescu),  Trans. Amer. Math. Soc. 361(6), 2913-2927, 2009.

Computable analysis of the abstract Cauchy problem in Banach spaces and its applications I (with K. Weihrauch),    MLQ Math. Log. Q. 53(4-5), 511-531, 2007.

Computable analysis of a boundary-value problem for the Korteweg-de Vries equation, Theory Comput. Syst., 41, 155-175, 2007.

An algorithm for computing fundamental solutions (with K. Weihrauch), SIAM J. Comput. 35(6), 1283-1294, 2006.

Computing Schrodinger propagators on type-2 Turing machines (with K. Weihrauch), J. Complexity 22(6), 918–935, 2006.

Computing the solution of the Korteweg-de Vries equation with arbitrary precision on Turing machines (with K. Weihrauch), Theoret. Comput. Sci., 332, 337-366, 2005.

Computability theory of generalized functions (with K. Weihrauch), J. ACM, 50(4), 469-505, 2003.

Is the wave propagator computable or can wave machines beat Turing machines (with K. Weihrauch)? Proc. London Math. Soc., 3(85), 312-332, 2002.


Member of Editorial Board, Computability, the Journal of the Association Computability in Europe ( Type:Editorial Service 08-2011 -To Present

Contact Information

5514 French Hall West
Phone: (513)556-4086