# Hausdorff Dimension of Sets of Generic Points for Non-statistical Dynamical Systems

## TL;DR

This paper investigates the Hausdorff dimension of sets of generic points in certain one-dimensional dynamical systems with neutral fixed points, revealing that measures with full Hausdorff dimension exist even without physical measures.

## Contribution

It demonstrates the existence of a simplex of measures with full Hausdorff dimension basins in non-statistical dynamical systems with neutral fixed points.

## Key findings

- Existence of measures with full Hausdorff dimension basins.
- Neutral fixed points prevent the existence of physical measures.
- Full Hausdorff dimension basins are characterized for these systems.

## Abstract

We consider one dimensional maps with several neutral fixed points that do not admit any physical measures. We show that there is simplex of measures so that every measure in this simplex has a basin which has full Hausdorff dimension.