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math.LO2021
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…
math.LO2021
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 $\…
math.DS2021★ 4 cited
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…