# A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set

## TL;DR

This paper constructs a specific self-similar dendrite in the plane with a one-point intersection property and a dense, countable post-critical set, revealing complex topological and dynamical features.

## Contribution

It introduces a novel example of a self-similar system with unique intersection and post-critical set properties not previously documented.

## Key findings

- The attractor is a plane dendrite containing [0,1].
- The post-critical set is countable and dense in a Cantor set.
- The system exhibits one point intersection property.

## Abstract

We build an example of a system $\mathcal{S}$ of similarities in $\mathbb{R}^2$ whose attractor is a plane dendrite $K\supset [0,1]$ which satisfies one point intersection property, while the post-critical set of the system $\mathcal{S}$ is a countable set whose natural projection to $K$ is dense in the middle-third Cantor set.