On the computational complexity of ordinary differential equations
Information and Control
Differential equations and dynamical systems
Differential equations and dynamical systems
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Hyperbolic Julia Sets are Poly-Time Computable
Electronic Notes in Theoretical Computer Science (ENTCS)
A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Lipschitz Continuous Ordinary Differential Equations are Polynomial-Space Complete
Computational Complexity - Selected papers from the 24th Annual IEEE Conference on Computational Complexity (CCC 2009)
| Hi-index | 5.23 |
As one of the seven open problems in the addendum to their 1989 book Computability in Analysis and Physics Pour-El and Richards (1989) [17], Pour-El and Richards asked, ''What is the connection between the computability of the original nonlinear operator and the linear operator which results from it?'' Yet at present, systematic studies of the issues raised by this question seem to be missing from the literature. In this paper, we study one problem in this direction: the Hartman-Grobman linearization theorem for ordinary differential equations (ODEs). We prove, roughly speaking, that near a hyperbolic equilibrium point x"0 of a nonlinear ODE x@?=f(x), there is a computable homeomorphism H such that H@?@f=L@?H, where @f is the solution to the ODE and L is the solution to its linearization x@?=Df(x"0)x.