Classification of connection graphs of global attractors for -equivariant parabolic equations

  • Carlos Rocha

    Universidade de Lisboa, Lisbon, Portugal
Classification of connection graphs of global attractors for $S^{1}$-equivariant parabolic equations cover
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Abstract

We consider the characterization of global attractors for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form , defined on the circle , for a class of reversible nonlinearities. Given two reversible nonlinearities, and , with the same lap signature, we prove the existence of a reversible homotopy , 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 to the trivial global attractor .

Cite this article

Carlos Rocha, Classification of connection graphs of global attractors for -equivariant parabolic equations. Port. Math. 82 (2025), no. 3/4, pp. 297–323

DOI 10.4171/PM/2144