Gauge theory with infinite group actions

热带几何将离散动力系统与自动机联系起来。我们用它来推导出相互不同的理性动力学之间的一个解析比较定理。将该方法应用于自动机群理论，特别是Burnside群，得到了无穷拟递归有理动力系统的一个新例子，构造了具有高度对称性的无限维几乎Kaehler流形上全纯曲线的模理论。作为应用，我们构造了作用在树上的群的哈密顿变形，并证明了对于某类哈密顿量，它们在我们的意义下总是一致无限的。

Tropical geometry connects discrete dynamical systems with automata. We used it to induce an analytic comparison theorem between mutually different rational dynamics or PDEs. We applied the method to theory of automata groups, particularly to Burnside groups and obtained a new example of infinitely quasi-recursive rational dynamical systems.We constructed moduli theory of holomorphic curves over infinite dimensional almost Kaehler manifolds with high symmetry. As an application, we constructed Hamiltonian deformation of groups acting on trees, and verified that for some class of Hamiltonians, they must be always uniformly infinite in ours sense.