TY - JOUR
T1 - Structural Stability of a Dynamical System Near a Non-Hyperbolic Fixed Point
AU - Bauerschmidt, Roland
AU - Brydges, David C.
AU - Slade, Gordon
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2015/4
Y1 - 2015/4
N2 - We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear ordinary differential equation in a Banach space of carefully weighted sequences. Using this, we prove existence and regularity of flows of the dynamical system which obey mixed initial and final boundary conditions. The class of dynamical systems we study, and the boundary conditions we impose, arise in a renormalization group analysis of the 4-dimensional weakly self-avoiding walk and the 4-dimensional n-component |φ|4 spin model.
AB - We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear ordinary differential equation in a Banach space of carefully weighted sequences. Using this, we prove existence and regularity of flows of the dynamical system which obey mixed initial and final boundary conditions. The class of dynamical systems we study, and the boundary conditions we impose, arise in a renormalization group analysis of the 4-dimensional weakly self-avoiding walk and the 4-dimensional n-component |φ|4 spin model.
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U2 - 10.1007/s00023-014-0338-0
DO - 10.1007/s00023-014-0338-0
M3 - Article
AN - SCOPUS:85027932326
SN - 1424-0637
VL - 16
SP - 1033
EP - 1065
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 4
ER -