Topological conjugacy for unimodal nonautonomous discrete dynamical systems

TL;DR

This paper introduces kneading sequences for nonautonomous discrete dynamical systems, demonstrating that these sequences serve as complete invariants for classifying systems up to topological conjugacy.

Contribution

It extends the concept of kneading sequences to nonautonomous systems and proves their effectiveness as invariants for topological conjugacy.

Findings

Kneading sequences are complete invariants for nonautonomous systems.

The paper establishes a correspondence between combinatorial data and topological conjugacy.

It advances the understanding of classification in nonautonomous dynamical systems.

Abstract

The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a complete invariant for topological conjugacy classes.