Difference between revisions of "Artin-Mazur zeta function"

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Let $\mathrm{Fix}(f^n)$ be the set of [[fixed points]] of the $n$th [[iterate]] $f^n$ of $f$. Let $\mathrm{Card}(Fix)(f^n)$ denote the [[cardinality]] of the set $\mathrm{Fix}(f^n)$. The Artin-Mazur zeta function is
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Let $\mathrm{Fix}(f^n)$ be the set of [[fixed points]] of the $n$th [[iterate]] $f^n$ of $f$. Let $\mathrm{Card}(\mathrm{Fix})(f^n)$ denote the [[cardinality]] of the set $\mathrm{Fix}(f^n)$. The Artin-Mazur zeta function is
 
$$\zeta_f(z)=\exp \left( \displaystyle\sum_{k=1}^{\infty} \mathrm{Card}(\mathrm{Fix})[f^n] \dfrac{z^n}{n} \right).$$
 
$$\zeta_f(z)=\exp \left( \displaystyle\sum_{k=1}^{\infty} \mathrm{Card}(\mathrm{Fix})[f^n] \dfrac{z^n}{n} \right).$$
  
 
=References=
 
=References=
 
[http://www.ihes.fr/~ruelle/PUBLICATIONS/%5B105%5D.pdf]
 
[http://www.ihes.fr/~ruelle/PUBLICATIONS/%5B105%5D.pdf]
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[[Category:SpecialFunction]]

Latest revision as of 18:52, 24 May 2016

Let $\mathrm{Fix}(f^n)$ be the set of fixed points of the $n$th iterate $f^n$ of $f$. Let $\mathrm{Card}(\mathrm{Fix})(f^n)$ denote the cardinality of the set $\mathrm{Fix}(f^n)$. The Artin-Mazur zeta function is $$\zeta_f(z)=\exp \left( \displaystyle\sum_{k=1}^{\infty} \mathrm{Card}(\mathrm{Fix})[f^n] \dfrac{z^n}{n} \right).$$

References

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