# Dynamically exotic contact spheres in dimensions $\geq 7$

## TL;DR

This paper constructs new examples of contact structures on high-dimensional spheres and products where all Reeb flows exhibit positive topological entropy, introducing algebraic growth of wrapped Floer homology as a key analytical tool.

## Contribution

It provides the first known examples of contact structures with universally positive entropy Reeb flows in dimensions greater than six, using a novel algebraic growth concept.

## Key findings

- All Reeb flows on the constructed contact structures have positive topological entropy.
- Introduction of algebraic growth of wrapped Floer homology as a stable geometric invariant.
- Demonstration of the existence of exotic contact structures in high dimensions.

## Abstract

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool for the study of the volume growth of Reeb flows we introduce the notion of algebraic growth of wrapped Floer homology. Its power stems from its stability under several geometric operations on Liouville domains.