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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.