Topological weak mixing and diffusion at all times for a class of Hamiltonian systems

TL;DR

This paper constructs examples of nearly integrable Hamiltonian systems demonstrating topological weak mixing and continuous diffusion, showcasing complex dynamical behaviors through advanced mathematical constructions.

Contribution

It introduces new examples of Hamiltonian systems with strong diffusion properties using AbC constructions with multiple frequencies.

Findings

Examples exhibit topological weak mixing.

Systems show diffusion at all times.

Construction method involves AbC with multiple frequencies.

Abstract

We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.