Renormalization destroys a finite time bifurcation in the $\Phi^4_2$ equation

Alexandra Blessing; Nicolas Perkowski; Chara Zhu

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arXiv · 2602.08460

Renormalization destroys a finite time bifurcation in the $\Phi^4_2$ equation

Alexandra Blessing·Nicolas Perkowski·Chara Zhu

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Abstract

We study the singular $\Phi^4_2$ 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 $\Phi^4_1$ equation. The proof relies on a support theorem for the stationary solution and its renormalized square.

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Alexandra Blessing, Nicolas Perkowski, Chara Zhu. 2026-02-09. Renormalization destroys a finite time bifurcation in the $\Phi^4_2$ equation. https://arxiv.org/abs/2602.08460

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