# Homoclinic points and Floer homology

## TL;DR

This paper introduces a Floer homology framework based on primary homoclinic points in dimension two, linking it to flux and symplectomorphism growth, with computed examples and an invariance theorem.

## Contribution

It establishes a novel Floer homology construction from homoclinic points and connects it to flux and dynamical growth in symplectic geometry.

## Key findings

- Constructed Floer homology from primary homoclinic points in dimension two
- Computed explicit examples demonstrating the theory
- Proved an invariance theorem for the homology

## Abstract

A new relation between homoclinic points and Lagrangian Floer homology is presented: In dimension two, we construct a Floer homology generated by primary homoclinic points. We compute two examples and prove an invariance theorem. Moreover, we establish a link to the (absolute) flux and growth of symplectomorphisms.