Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.15581 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911003768258560 |
|---|---|
| author | Rocha, Carlos |
| author_facet | Rocha, Carlos |
| contents | We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible nonlinearities. Given two reversible nonlinearities, $f_0$ and $f_1$, with the same lap signature, we prove the existence of a reversible homotopy $f_τ, 0\leτ\le 1$, which preserves all heteroclinic connections. Consequently, we obtain a classification of the connection graphs of global attractors in the class of reversible nonlinearities. We also describe bifurcation diagrams which reduce a global attractor $A_1$ to the trivial global attractor $A_0=\{0\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of connection graphs of global attractors for $S^1$-equivariant parabolic equations Rocha, Carlos Dynamical Systems 37L30, 35K57, 34C25 We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible nonlinearities. Given two reversible nonlinearities, $f_0$ and $f_1$, with the same lap signature, we prove the existence of a reversible homotopy $f_τ, 0\leτ\le 1$, which preserves all heteroclinic connections. Consequently, we obtain a classification of the connection graphs of global attractors in the class of reversible nonlinearities. We also describe bifurcation diagrams which reduce a global attractor $A_1$ to the trivial global attractor $A_0=\{0\}$. |
| title | Classification of connection graphs of global attractors for $S^1$-equivariant parabolic equations |
| topic | Dynamical Systems 37L30, 35K57, 34C25 |
| url | https://arxiv.org/abs/2403.15581 |