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

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1033-1065
Number of pages33
JournalAnnales Henri Poincare
Issue number4
StatePublished - Apr 2015

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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