Year: 2019
Type: article
Abstract: Motivated by the normal form of a fast–slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking trajectories in the vicinity of the singularity we show, how the slow manifold extends beyond the singular point and give an estimate on the contraction rate of a transition mapping. The proof relies on the blow-up method suitably adapted to the discrete setting where precise estimates for a cubic map in the central rescaling chart make a key technical contribution.
Authors: Luca Arcidiacono, Maximilian Engel, Christian Kuehn
Institution: Technical University of Munich
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2965718394