Renormalization destroys a finite time bifurcation in the $Φ^4_2$ equation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910016444825600 |
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| author | Blessing, Alexandra Perkowski, Nicolas Zhu, Chara |
| author_facet | Blessing, Alexandra Perkowski, Nicolas Zhu, Chara |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08460 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalization destroys a finite time bifurcation in the $Φ^4_2$ equation Blessing, Alexandra Perkowski, Nicolas Zhu, Chara Probability 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. |
| title | Renormalization destroys a finite time bifurcation in the $Φ^4_2$ equation |
| topic | Probability |
| url | https://arxiv.org/abs/2602.08460 |