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nLab > Latest Changes: Ruelle zeta function

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2015

    am beginning to add some genuine content to Ruelle zeta function (which used to just redirect to zeta function of a dynamical system which in turn is no more that a stub)

    not done yet

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJun 30th 2015
    • (edited Jun 30th 2015)

    The page zeta function of a dyanimcal system says

    When interpreting the Frobenius morphisms that appear in the Artin L-functions geometrically as flows (as discussed at Borger’s arithmetic geometry – Motivation) then this induces an evident analog of zeta function of a dynamical system.

    Could we replace “induces” by “motivates”? Confusingly to a mathematician, inducing is usually about a formal procedure how to transfer the information in one structure to get another structure (induced topology, induced representation etc.); but I suspect that here it is just an analogical thinking and not a priori well defined procedure of transfering the definition to another realm…

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 3rd 2015
    • (edited Jul 3rd 2015)

    Also, the Ruelle zeta function is defined more widely than for hyperbolic manifolds of odd dimension. I noticed this having commented on a post on a formula of Feynman for the Ising model. So I’ve added a broader definition.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 19th 2016

    Added the notes Dynamical zeta functions on the arXiv today as a reference.

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