# Stationary states of the cubic conformal flow on $\mathbb{S}^3$

@article{Bizo2018StationarySO, title={Stationary states of the cubic conformal flow on \$\mathbb\{S\}^3\$}, author={Piotr Bizoń and Dominika Hunik-Kostyra and Dmitry E. Pelinovsky}, journal={arXiv: Mathematical Physics}, year={2018} }

We consider the resonant system of amplitude equations for the conformally invariant cubic wave equation on the three-sphere. Using the local bifurcation theory, we characterize all stationary states that bifurcate from the first two eigenmodes. Thanks to the variational formulation of the resonant system and energy conservation, we also determine variational characterization and stability of the bifurcating states. For the lowest eigenmode, we obtain two orbitally stable families of the…

## 6 Citations

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### Melonic Turbulence

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We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear…

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