Nonlinear Sciences > Chaotic Dynamics
[Submitted on 15 Feb 2021 (v1), last revised 16 Feb 2021 (this version, v2)]
Title:Revealing the phase space structure of Hamiltonian systems using the action
View PDFAbstract:In this work, we analyse the properties of the Maupertuis' action as a tool to reveal the phase space structure for Hamiltonian systems. We construct a scalar field with the action's values along the trajectories in the phase space. The different behaviour of the trajectories around important phase space objects like unstable periodic orbits, their stable and unstable manifolds, and KAM islands generate characteristic patterns on the scalar field constructed with the action. Using these different patterns is possible to identify the skeleton of the phase space and understand the dynamics. Also, we present a simple argument based on the conservation of the energy and the behaviour of the trajectories to understand the values of their actions. In order to show how this tool reveals the phase space structures and its effectiveness, we compare the scalar field constructed with the actions with Poincare maps for the same set of initial conditions in the phase space of an open Hamiltonian system with 2 degrees of freedom.
Submission history
From: Makrina Agaoglou [view email][v1] Mon, 15 Feb 2021 13:37:58 UTC (2,565 KB)
[v2] Tue, 16 Feb 2021 16:20:57 UTC (2,566 KB)
Current browse context:
nlin.CD
Change to browse by:
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.