Existence of C^{K}-invariant foliations for Lorenz type maps

TL;DR

This paper proves that under certain conditions, Lorenz-type maps possess invariant foliations that are smooth and can be associated with one-dimensional transformations, extending previous results.

Contribution

It establishes the existence of C^{k} invariant foliations for Lorenz-type maps under conditions similar to earlier work, linking them to one-dimensional dynamics.

Findings

Existence of C^{k} invariant foliations for Lorenz-type maps.

Construction of a C^{k} one-dimensional transformation associated with the map.

Extension of previous results to broader conditions.

Abstract

In this paper under similar conditions to that Shaskov and Shil'nikov [1994] we show that a C^{k+1} Lorenz-type map T has a C^{k} foliation which is invariant under T. This allows us to associate T to a C^{k} one-dimensional transformation.