Godel Diffeomorphisms Article Swipe
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Matthew Foreman
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YOU?
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· 2020
· Open Access
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· DOI: https://doi.org/10.48550/arxiv.2009.06735
· OA: W3086265755
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2009.06735
· OA: W3086265755
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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