Algebraic Number Theory and Hamiltonian Chaos

  • F. Vivaldi
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 47)


Three great themes were developed in algebraic number theory during the nineteenth century, namely quadratic forms, algebraic numbers and ideals, which call to mind the names of Gauss, Kummer, and Dedekind, respectively. They represent three ways of dealing with one and the same problem, the failure of the fundamental theorem of arithmetic (unique factorization into primes) in algebraic number fields. Had the fundamental theorem been valid, Gauss would have probably answered any conceivable question about binary quadratic forms while in his teens, and Kummer would have proved Fermat’s last theorem. As to ideal theory, it wouldn’t have been developed for quite a while.


Periodic Orbit Prime Ideal Chaotic Dynamic Characteristic Polynomial Algebraic Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • F. Vivaldi
    • 1
  1. 1.School of Mathematical Sciences, Queen Mary CollegeUniversity of LondonLondonUK

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