42 citations · 109 across the 13 of their papers we have counts for
6 papers · 1 filter
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 $\…
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…
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…