Krieger, JoachimNakanishi, KenjiSchlag, Wilhelm2012-10-152012-10-152012-10-15201410.1007/s00220-014-1900-9https://infoscience.epfl.ch/handle/20.500.14299/86134WOS:000333055600010For the critical focusing wave equation $\square u=u^5$ on $\mathbb{R}^{3+1}$ in the radial case, we establish the role of the “center stable” manifold $\Sigma$ constructed in [18] near the ground state $(W,0)$ as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo´n, Chmaj, Tabor [3]. The underlying topology is stronger than the energy norm.critical wave equationhyperbolic dynamicsblowupscatteringstabilityinvariant manifoldtext::journal::journal article::research article