Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An exercise in experimental mathematics: calculation of the algebraic entropy of a map

C. M. Viallet

TL;DR

The use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces is illustrated, where a complete proof is still awaited, but where different approaches are in such perfect agreement that no-one can trust they get to an exact result.

Abstract

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where different approaches are in such perfect agreement that we can trust we get to an exact result. This is an instructive example of experimental mathematics.

An exercise in experimental mathematics: calculation of the algebraic entropy of a map

TL;DR

The use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces is illustrated, where a complete proof is still awaited, but where different approaches are in such perfect agreement that no-one can trust they get to an exact result.

Abstract

We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where different approaches are in such perfect agreement that we can trust we get to an exact result. This is an instructive example of experimental mathematics.
Paper Structure (8 sections, 27 equations)

This paper contains 8 sections, 27 equations.

Table of Contents

  1. Introduction: algebraic entropy of maps
  2. Warm-up: a well studied two dimensional map
  3. A more challenging map
  4. Method 0
  5. Method 1
  6. Method 2
  7. Why did Method 1 not work?
  8. Conclusion