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

PhD: University of Wisconsin at Madison 1991

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

Peer Reviewed Publications

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

Robust non-computability of dynamical systems and computability of robust dynamical systems (with D.S. Graca), Logical Methods in Computer Science  (https://lmcs.episciences.org),  20(2):19:1-19:27, 2024.

Computing the exact number of periodic orbits for planar flows (with D. S. Graca),  Transactions of the American Mathematical Society, 
375:5491-5538, 2022.

Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines (with D.S. Graca), Computability - The Journal of the Association Computability in Europe  (http://www.computability.de/journal/),  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 (http://www.computability.de/journal/) Type:Editorial Service 08-2011 -To Present

5514 French Hall West
Phone: (513)556-4086
zhongn@ucmail.uc.edu