The parameterization method for center manifolds

2019/05/01 by Jan Bouwe van den Berg, Berg, Jan Bouwe van den, Wouter Hetebrij +3 · 1 citation
Engineering · #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Gear and Bearing Dynamics Analysis #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.1905.00264

openalex publication_date 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a generalization of the parameterization method, introduced by Cabré, Fontich and De la Llave, to center manifolds associated to non-hyperbolic fixed points of discrete dynamical systems. As a byproduct, we find a new proof for the existence and regularity of center manifolds. However, in contrast to the classical center manifold theorem, our parameterization method will simultaneously obtain the center manifold and its conjugate center dynamical system. Furthermore, we will provide bounds on the error between approximations of the center manifold and the actual center manifold, as well as bounds for the error in the conjugate dynamical system.

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• Reduced order modelling of Hopf bifurcations for the Navier-Stokes equations through invariant manifolds

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