The regularized free fall I -- Index computations

TL;DR

This paper extends the Conley-Zehnder index to delay differential equations and establishes the equivalence of Morse and Conley-Zehnder indices in this context.

Contribution

It generalizes the Conley-Zehnder index for delay equations and proves the Morse index equals the normalized Conley-Zehnder index.

Findings

Conley-Zehnder index is extended to delay equations.

Morse index equals normalized Conley-Zehnder index.

Provides a new index computation method for delay equations.

Abstract

Main results are, firstly, a generalization of the Conley-Zehnder index from ODEs to the delay equation at hand and, secondly, the equality of the Morse index and the clockwise normalized Conley-Zehnder index.