An N-to-1 Smale Horseshoe

TL;DR

This paper extends the Conley-Moser Theorem to N-to-1 local diffeomorphisms, enabling symbolic encoding of generalized horseshoe maps and confirming their structural stability.

Contribution

It introduces an extension of the Conley-Moser Theorem for N-to-1 maps and demonstrates their structural stability through symbolic dynamics.

Findings

Extended Conley-Moser Theorem for N-to-1 maps

Symbolic encoding of generalized N-to-1 horseshoe maps

Verification of structural stability

Abstract

In this work we extend the Conley-Moser Theorem for $N$-to-1 local diffeomorphisms. By the aim of some extended symbolic dynamics we encode generalized $N$-to-1 horseshoe maps and as a corollary their structural stability is verified.