On the K-property of quantized Arnold cat maps

TL;DR

This paper proves that certain quantized Arnold cat maps exhibit K-property, demonstrating their complex chaotic behavior through a strictly local entropy decomposition based on Voiculescu's construction.

Contribution

It establishes the K-property for some quantized Arnold cat maps using a new strictly local entropy decomposition approach.

Findings

Proves some quantized Arnold cat maps are entropic K-systems.

Introduces a strictly local decomposition based on Voiculescu.

Addresses previous issues with non-local optimal decompositions.

Abstract

We prove that some quantized Arnold cat maps are entropic K-systems. This result was formulated by H. Narnhofer[1], but the fact that the optimal decomposition for the multi-channel entropy constructed there is not strictly local was not appropriately taken care of. We propose a strictly local decomposition based on a construction of Voiculescu.