Geometric scattering monodromy

TL;DR

This paper establishes geometric conditions under which the integral mapping of a Liouville integrable Hamiltonian system exhibits scattering monodromy, linking it to the standard focus-focus system through complex Morse theory.

Contribution

It provides geometric criteria for scattering monodromy in integrable systems and relates it to the well-understood focus-focus case using complex Morse analysis.

Findings

Scattering monodromy occurs under specific geometric conditions.

Scattering monodromy of a general system matches that of the standard focus-focus system.

Complex Morse lemma is used to establish the equivalence.

Abstract

In this paper we give geometric conditions so that the integral mapping of a Liouville integrable Hamiltonian system with a focus-focus equilibrium point has scattering monodromy. Using a complex version of the Morse lemma, we show that scattering monodromy is the same as the scattering monodromy of the standard focus-focus system.