English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For one variable rational function $\phi\in K(z)$ over a field $K$, we candefine a discrete dynamical system by regarding $\phi$ as a self morphism of$\mathbb{P}_{K}^{1}$. Hatjispyros and Vivaldi defined a dynamical zeta functionfor this dynamical system using multipliers of periodic points, that is, aninvariant which indicates the local behavior of dynamical systems. In thispaper, we prove the rationality of dynamical zeta functions of this type for alarge class of rational functions $\phi\in K(z)$. The proof here relies onWoods Hole fixed point formula and some basic facts on the trace of a linearmap acting on cohomology of a coherent sheaf on $\mathbb{P}_{K}^{1}$.

The rationality of dynamical zeta functions and Woods Hole fixed point formula