TY - JOUR
T1 - The parameterization method for center manifolds
AU - van den Berg, Jan Bouwe
AU - Hetebrij, Wouter
AU - Rink, Bob
PY - 2020/7/15
Y1 - 2020/7/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85079196290&partnerID=8YFLogxK
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U2 - 10.1016/j.jde.2020.01.033
DO - 10.1016/j.jde.2020.01.033
M3 - Article
AN - SCOPUS:85079196290
VL - 269
SP - 2132
EP - 2184
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 3
ER -