New partially hyperbolic dynamical systems I

TL;DR

This paper introduces a novel method for constructing partially hyperbolic diffeomorphisms on closed manifolds, demonstrating the existence of such systems on simply connected closed manifolds, which was previously unknown.

Contribution

The paper presents a new construction technique for partially hyperbolic diffeomorphisms and shows their existence on simply connected closed manifolds, expanding the class of known examples.

Findings

Existence of partially hyperbolic diffeomorphisms on simply connected closed manifolds.

Introduction of a new construction method for such dynamical systems.

Demonstration of the method's effectiveness through explicit examples.

Abstract

We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.