Semitoric Families on Pentagon Spaces

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Liu, Yichen, Si, Aerim
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866915824007118848
author Liu, Yichen
Si, Aerim
author_facet Liu, Yichen
Si, Aerim
contents Semitoric systems are a special type of 4-dimensional integrable system where one of the functions is the moment map of a Hamiltonian $S^1$-action. While their classification is well understood thanks to the work of Pelayo and V{ũ} Ng\d{o}c, relatively few explicit examples are known. Recently, Le Floch and Palmer introduced semitoric transition families in which a singular point transitions between elliptic-elliptic type and focus-focus type as the parameter varies. In this paper, we construct new semitoric transition families on pentagon spaces by interpolating two semitoric systems of toric type. More precisely, we exhibit semitoric transition families, each with at least one transition point, on pentagon spaces of different diffeotypes, all defined by the same explicit interpolation formula.
format Preprint
id arxiv_https___arxiv_org_abs_2510_11624
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Semitoric Families on Pentagon Spaces
Liu, Yichen
Si, Aerim
Symplectic Geometry
Dynamical Systems
37J35, 53D20
Semitoric systems are a special type of 4-dimensional integrable system where one of the functions is the moment map of a Hamiltonian $S^1$-action. While their classification is well understood thanks to the work of Pelayo and V{ũ} Ng\d{o}c, relatively few explicit examples are known. Recently, Le Floch and Palmer introduced semitoric transition families in which a singular point transitions between elliptic-elliptic type and focus-focus type as the parameter varies. In this paper, we construct new semitoric transition families on pentagon spaces by interpolating two semitoric systems of toric type. More precisely, we exhibit semitoric transition families, each with at least one transition point, on pentagon spaces of different diffeotypes, all defined by the same explicit interpolation formula.
title Semitoric Families on Pentagon Spaces
topic Symplectic Geometry
Dynamical Systems
37J35, 53D20
url https://arxiv.org/abs/2510.11624