论文标题
$ \ mathbf {r}^5 $ to $ s^5 $从$ \ mathbf {r}^5 $ to $ s^5 $
Supercritical equivariant biharmonic maps from $\mathbf{R}^5$ into $S^5$
论文作者
论文摘要
我们研究超临界$ o（d）$ - 等效的Biharmonic地图，重点是$ d = 5 $，其中$ d $是域的维度。我们将来自$ \ Mathbf {r}^5 $的非平凡地模式地图的表征分为$ s^5 $，为相关动力学系统的异质轨道。此外，我们证明了这种非平凡的白马图的存在。最后，与谐波地图类似物形成鲜明对比的是，我们表明了$ b^5（0，1）$到$ s^5 $无限多次多次的$ s^5 $的$ b^5（0，1）$的存在。
We study supercritical $O(d)$-equivariant biharmonic maps with a focus on $d = 5$, where $d$ is the dimension of the domain. We give a characterisation of non-trivial equivariant biharmonic maps from $\mathbf{R}^5$ into $S^5$ as heteroclinic orbits of an associated dynamical system. Moreover, we prove the existence of such non-trivial equivariant biharmonic maps. Finally, in stark contrast to the harmonic map analogue, we show the existence of an equivariant biharmonic map from $B^5(0, 1)$ into $S^5$ that winds around $S^5$ infinitely many times.
