Zeta-functions of renormalizable sub-Lorenz templates

TL;DR

This paper explores the zeta functions associated with sub-Lorenz templates generated by renormalizable Lorenz maps, expressing them through the zeta functions of related templates and renormalization maps.

Contribution

It provides a novel description of Williams and twist zeta functions for renormalizable sub-Lorenz templates using renormalization theory.

Findings

Expressed zeta functions in terms of renormalized templates

Connected zeta functions to renormalization types

Enhanced understanding of sub-Lorenz template dynamics

Abstract

We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.