Renormalization destroys a finite time bifurcation in the $Φ^4_2$ equation
Abstract
We study the singular $Φ^4_2$ equation at a pitchfork bifurcation of the underlying deterministic dynamics. To this aim, we linearize the SPDE along its stationary solution and show that the support of its finite-time Lyapunov exponents (FTLEs) is the real line, regardless of the bifurcation parameter and in sharp contrast to the non-singular $Φ^4_1$ equation. The proof relies on a support theorem for the stationary solution and its renormalized square.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Mathematical Physics Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint