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

## Professor

## Professor

### French Hall

5514

A&S Mathematical Sciences - 0025

## Education

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: https://doi.org/10.1090/tran/8644.

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.** Vo*lume 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.

## Service

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

## Contact Information

5514 French Hall West

Phone: (513)556-4086

zhongn@ucmail.uc.edu