标题： 具有有界条件的动态系统与$C^{*}$-代数 显示英文标题

标题： Dynamical Systems with Bounded Condition and $C^{*}$-algebras

摘要： 通过引入映射的完全唯一性条件，我们建立了不变集族与$q x{+}d$函数（例如$3 x{+}1$映射，也称为Collatz映射）之间的双射对应关系，其中$q$和$d$是任意正奇数，以及相关$C^{*}$代数的约化子空间族。这扩展了Collatz猜想（也称为$3 n{+}1$问题）与其相关$C^{*}$代数的不可约性之间的联系。我们还介绍了在有界条件下保持这些动力系统结构的动力系统之间的同态。 我们证明了对于具有有界条件的动态系统之间的每个同构，它们相关的$C^{*}$-代数之间的同构存在。 显示英文摘要

摘要： By introducing the totally uniqueness condition for maps, we establish a one-to-one correspondence between the family of invariant sets for the $q x{+}d$-function (e.g. the $3 x{+}1$-map, also known as the Collatz map), where $q$ and $d$ are arbitrary positive odd numbers, and the family of reducing subspaces for the associated $C^{*}$-algebra. This extends the connection between the Collatz conjecture (also known as the $3 n{+}1$-problem) and the irreducibility of its associated $C^{*}$-algebra. We also introduce homomorphisms between dynamical systems with bounded conditions that preserve the structures of these dynamical systems. We prove the existence of an isomorphism between their associated $C^{*}$-algebras is proven for every isomorphism between dynamical systems with bounded condition.