4 citations · 9 across the 10 of their papers we have counts for
10 papers
Robust non-computability of dynamical systems and computability of robust dynamical systems
Daniel S. Graça, Ning Zhong
In this paper, we examine the relationship between the stability of the dynamical system and the computability of its basins of attraction. We present a computabl…
Robustness of non-computability
Daniel S. Graça, Ning Zhong
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic d…
Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines
Daniel S. Graça, Ning Zhong
In this paper, we analyze the problem of finding the minimum dimension such that a closed-form analytic map/ordinary differential equation can simulate a Turing machine over $\…
Computing the exact number of periodic orbits for planar flows
Daniel S. Graça, Ning Zhong
In this paper, we consider the problem of determining the \emph{exact} number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. U…
The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable
Daniel S. Graça, Ning Zhong
In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow defined on the closed unit disk, outputs the exact number…
Computability of the Solutions to Navier-Stokes Equations via Recursive Approximation
Shu-Ming Sun, Ning Zhong, Martin Ziegler
As one of the seven open problems in the addendum to their 1989 book "Computability in Analysis and Physics", Pour-El and Richards proposed ``... the recursion theoretic study of p…
Computing geometric Lorenz attractors with arbitrary precision
Daniel Graca, Cristobal Rojas, Ning Zhong
The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous)…
An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable
Daniel S. Graça, Ning Zhong
In many applications one is interested in finding the stability regions (basins of attraction) of some stationary states (attractors). In this paper we show that one cannot compute…
Computability, Noncomputability, and Hyperbolic Systems
Daniel S. Graca, Ning Zhong, Jorge Buescu
In this paper we study the computability of the stable and unstable manifolds of a hyperbolic equilibrium point. These manifolds are the essential feature which characterizes a hyp…
Proceedings Seventh International Conference on Computability and Complexity in Analysis
Xizhong Zheng, Ning Zhong
This volume of the Electronic Proceedings in Theoretical Computer Science (EPTCS) contains extended abstracts of talks to be presented at the Seventh International Conference on Co…