# Dynamical invariants of monomial correspondences

## TL;DR

This paper investigates dynamical invariants of toric correspondences, deriving formulas for dynamical degrees, analyzing degree growth, and computing height growth ratios using algebraic geometry and arithmetic methods.

## Contribution

It provides explicit formulas for dynamical degrees and links degree growth with log-concavity, advancing understanding of toric correspondence dynamics.

## Key findings

- Derived a formula for dynamical degrees
- Linked degree growth to log-concavity conditions
- Computed asymptotic height growth ratios

## Abstract

We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict log-concavity condition on the dynamical degrees and compute the asymptotic ratio of the growth of heights of points of such correspondences.