AbstractState space discretization occurs in the discrete finite arithmetic of a computer. When a dynamical system is simulated by numerical computations, it consequently evolves in a discretized space of this kind. Where attractors are seen in the simulation, what is their relation to the theoretical structures? If a theoretical attractor occurs, should we expect always to see a computational attractor? We address these questions by giving sufficient conditions for a discretized attractor to be present, and show that it converges to the true attractor in the sense of convergence of compact sets in the Hausdorff metric
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into f...
We present a survey of the recent applications of continuous domains for providing simple computatio...
This book looks at dynamics as an iteration process where the output of a function is fed back as an...
AbstractState space discretization occurs in the discrete finite arithmetic of a computer. When a dy...
Investigates what can go wrong when dynamical systems are modelled with a computer. Number theoretic...
Abstract: We investigate necessary and sucient conditions for the convergence of attractors of discr...
Abstract. This paper concerns the link between the dynamical behaviour of a dynam-ical system and th...
Abstract. The standard upper and lower semicontinuity results for discretized attractors [22], [13],...
AbstractComputer simulations of dynamical systems contain discretizations, where finite machine arit...
ABSTRACT. The algebraic structure of the attractors in a dynamical system deter-mine much of its glo...
Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic r...
This work focuses on the preservation of attractors and saddle points of ordinary differential equat...
dedicated to professor jack hale on the occasion of his 70th birthday In this paper we prove that th...
This paper is a study of the global structure of the attractors of a dynamical system. The dynamical...
The effect of temporal discretisation on dissipative differential equations is analysed. We discuss ...
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into f...
We present a survey of the recent applications of continuous domains for providing simple computatio...
This book looks at dynamics as an iteration process where the output of a function is fed back as an...
AbstractState space discretization occurs in the discrete finite arithmetic of a computer. When a dy...
Investigates what can go wrong when dynamical systems are modelled with a computer. Number theoretic...
Abstract: We investigate necessary and sucient conditions for the convergence of attractors of discr...
Abstract. This paper concerns the link between the dynamical behaviour of a dynam-ical system and th...
Abstract. The standard upper and lower semicontinuity results for discretized attractors [22], [13],...
AbstractComputer simulations of dynamical systems contain discretizations, where finite machine arit...
ABSTRACT. The algebraic structure of the attractors in a dynamical system deter-mine much of its glo...
Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic r...
This work focuses on the preservation of attractors and saddle points of ordinary differential equat...
dedicated to professor jack hale on the occasion of his 70th birthday In this paper we prove that th...
This paper is a study of the global structure of the attractors of a dynamical system. The dynamical...
The effect of temporal discretisation on dissipative differential equations is analysed. We discuss ...
This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into f...
We present a survey of the recent applications of continuous domains for providing simple computatio...
This book looks at dynamics as an iteration process where the output of a function is fed back as an...