The disintegration of measures with periodic repetitive pattern

TL;DR

This paper introduces a new class of measures called measures with periodic repetitive pattern in skew-product systems, showing they have atomic disintegration along fibers, expanding understanding of non-hyperbolic measures.

Contribution

It defines measures with periodic repetitive pattern in skew-products and proves their atomic disintegration along central fibers, including non-hyperbolic cases.

Findings

Measures with periodic repetitive pattern have atomic disintegration.

Includes non-hyperbolic measures in the analysis.

Provides new insights into measure disintegration in skew-products.

Abstract

In the context of locally constant skew-products over the shift with circle fiber maps we introduce the notion of measures with periodic repetitive pattern, inspired by \cite{GorIlyKleNal:05} and which includes the non-hyperbolic measures they construct. We prove that these measures have atomic disintegration along the central fibers.