Godel Diffeomorphisms

Matthew Foreman

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arXiv · 2009.06735

Godel Diffeomorphisms

Matthew Foreman

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Abstract

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.

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Matthew Foreman. 2020-09-14. Godel Diffeomorphisms. https://arxiv.org/abs/2009.06735

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