Annales Henri Poincaré

, Volume 16, Issue 4, pp 1033–1065 | Cite as

Structural Stability of a Dynamical System Near a Non-Hyperbolic Fixed Point

  • Roland Bauerschmidt
  • David C. BrydgesEmail author
  • Gordon Slade


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.


Banach Space Structural Stability Spin Model External Parameter Solution Operator 
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Roland Bauerschmidt
    • 1
    • 2
  • David C. Brydges
    • 1
    Email author
  • Gordon Slade
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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