论文标题
dodel差异性
Godel Diffeomorphisms
论文作者
论文摘要
平滑动力学的一个基本问题是确定系统是否可以与其逆区分开，即，平滑的差异性$ t $是否同构对$ t^{ - 1} $。我们表明，这个问题足够笼统地，要求其特定选择$ t $等效于众所周知的数字理论猜想的有效性，包括Riemann假设和Goldbach的猜想。此外，人们可以产生可计算的差异性$ t $，以便$ t $同构至$ t^{ - 1} $的问题独立于ZFC。
A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism $T$ is isomorphic to $T^{-1}$. We show that this problem is sufficiently general that asking it for particular choices of $T$ is equivalent to the validity of well-known number theoretic conjectures including the Riemann Hypothesis and Goldbach's conjecture. Further one can produce computable diffeomorphisms $T$ such that the question of whether $T$ is isomorphic to $T^{-1}$ is independent of ZFC.
