论文标题
混沌subriemannian Geodesic Flow $ J^2（\ Mathbb {r}^2，\ Mathbb {r}）$
Chaotic subRiemannian geodesic flow in $J^2(\mathbb{R}^2,\mathbb{R})$
论文作者
论文摘要
两个真实变量的实际功能的$ 2 $ jet的空间，由$ j^2（\ mathbb {r}^2，\ mathbb {r}）$表示，承认了一个metabelian carnot group的结构，因此$ j^2（\ mathbb {\ mathb {r}^2，\ r}^2，\ mathbb^ab and ab abel a a abel a n norkal a n norkal a a a a rucce $ \ mathbb {a} $。作为任何次 - riemannian歧管，$ j^2（\ mathbb {r}^2，\ mathbb {r}）$具有关联的汉密尔顿测量流。 $ \ mathbb {a} $ on $ t^*j^2（\ mathbb {r}^2，\ mathbb {r}）$在$ t^*j^2上的hamiltonian动作，在$ t^*\ mathcal {h} \ simeq \ simeq oon o y Mathbb {r}）上产生减少的hamiltonian $h_μ$ t^*（j^2（\ mathbb {r}^2，\ mathbb {r}）/\ mathbb {a}）$，其中$h_μ$是二维欧几里得空间。该论文致力于证明减少的Hamiltonian $H_μ$不可通过Meromormormorphic函数以$μ$的值进行。该结果表明$ j^{2}上的sub-riemannian Geodesic Flow（\ Mathbb {r}^2，\ Mathbb {r}）$不是Meromororphistable可以集成。
The space of $2$-jets of a real function of two real variables, denoted by $J^2(\mathbb{R}^2,\mathbb{R})$, admits the structure of a metabelian Carnot group, so $J^2(\mathbb{R}^2,\mathbb{R})$ has a normal abelian sub-group $\mathbb{A}$. As any sub-Riemannian manifold, $J^2(\mathbb{R}^2,\mathbb{R})$ has an associated Hamiltonian geodesic flow. The Hamiltonian action of $\mathbb{A}$ on $T^*J^2(\mathbb{R}^2,\mathbb{R})$ yields the reduced Hamiltonian $H_μ$ on $T^*\mathcal{H} \simeq T^*(J^2(\mathbb{R}^2,\mathbb{R})/\mathbb{A})$, where $H_μ$ is a two-dimensional Euclidean space. The paper is devoted to proving that reduced Hamiltonian $H_μ$ is non-integrable by meromorphic functions for some values of $μ$. This result suggests the sub-Riemannian geodesic flow on $J^{2}(\mathbb{R}^2,\mathbb{R})$ is not meromorphically integrable.
