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

In this paper we address the problem of computing $\text{deg}(f^n)$, thedegrees of iterates of a birational map$f:\mathbb{P}^N\rightarrow\mathbb{P}^N$. For this goal, we develop a methodbased on two main ingredients: the factorization of a polynomial underpull-back of $f$, based on local indices of a polynomial associated to blow-upsused to resolve the contraction of hypersurfaces by $f$, and the propagation ofthese indices along orbits of $f$.  For maps admitting algebraically stable modifications $f_X:X\rightarrow X$,where $X$ is a variety obtained from $\mathbb P^N$ by a finite number ofblow-ups, this method leads to an algorithm producing a finite system ofrecurrent equations relating the degrees and indices of iterated pull-backs oflinear polynomials. We illustrate the method by three representativetwo-dimensional examples. It is actually applicable in any dimension, and wewill provide a number of three-dimensional examples as a separate companionpaper.

Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups I. General theory and 2D examples