An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable

2014/09/03 by Graça, Daniel S., Zhong, Ning
#F.4.1 #FOS: Mathematics #Logic (math.LO) #Primary: 03D78 #Secondary: 68Q17

paper · doi:10.48550/arxiv.1409.1163

Abstract

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, in general, the basins of attraction of even very regular systems, namely analytic systems with hyperbolic asymptotically stable equilibrium points. To prove the main theorems, a new method for embedding a discrete-time system into a continuous-time system is developed.

Related

• On the basins of attraction of the regular autonomous asynchronous systems
• Robust approximation algorithms for the detection of attraction basins in dynamical systems
• Computability, Noncomputability, and Hyperbolic Systems
• Evaluation of the Region of Attractions of Higher Dimensional Hyperbolic Systems using the Extended Dynamic Mode Decomposition
• Methods for determination and approximation of domains of attraction in the case of autonomous discrete dynamical systems