2020/09/14 by Matthew Foreman, Foreman, Matthew
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #03B30 #03D80 #03E35 #37E30 #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Fractal and DNA sequence analysis #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2009.06735
openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.