The Cyclic Hopf H mod K Theorem

Adrian C. Murza

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arXiv · 1503.05118

The Cyclic Hopf H mod K Theorem

Adrian C. Murza

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Abstract

The $H~\mathrm{mod}~K$ theorem gives all possible periodic solutions in a $\Gamma-$equivariant dynamical system, based on the group-theoretical aspects. In addition, it classifies the spatio temporal symmetries that are possible. By the contrary, the equivariant Hopf theorem guarantees the existence of families of small-amplitude periodic solutions bifurcating from the origin for each $\mathbf{C}-$axial subgroup of $\Gamma\times\mathbb{S}^1.$ In this paper we identify which periodic solution types, whose existence is guaranteed by the $H~\mathrm{mod}~K$ theorem, are obtainable by Hopf bifurcation, when the group $\Gamma$ is finite cyclic.

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Adrian C. Murza. 2015-03-17. The Cyclic Hopf H mod K Theorem. https://arxiv.org/abs/1503.05118

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