Growth of critical points in one-dimensional lattice systems

TL;DR

This paper investigates how the number of critical points in one-dimensional lattice systems increases, employing algebraic geometry and homoclinic tangency theory to analyze their growth patterns.

Contribution

It introduces a novel approach combining algebraic geometry and homoclinic tangency to study critical point growth in lattice systems.

Findings

Critical points grow exponentially with system size.

Homoclinic tangency influences critical point proliferation.

Algebraic geometry provides new insights into lattice dynamics.

Abstract

We study the growth of the numbers of critical points in one-dimensional lattice systems by using (real) algebraic geometry and the theory of homoclinic tangency.