Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Dynamical Systems

arXiv:math/0306392 (math)
[Submitted on 27 Jun 2003]

Title:Vanishing Twist near Focus-Focus Points

Authors:Holger R. Dullin (1), Vu Ngoc San (2) ((1) Loughborough University and Universität Bremen, (2) Université Grenoble)
View PDF
Abstract: We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this we also show that the frequency map is non-degenerate for every point in a neighborhood of a focus-focus point.
Comments: 13 pages
Subjects: Dynamical Systems (math.DS); Symplectic Geometry (math.SG); Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 37J35; 37J15; 37J40; 70H06; 70H08; 37G20
Cite as: arXiv:math/0306392 [math.DS]
  (or arXiv:math/0306392v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.math/0306392
Journal reference: Nonlinearity, 17:1777--1786, 2004
Related DOI: https://doi.org/10.1088/0951-7715/17/5/012

Submission history

From: Holger R. Dullin [view email]
[v1] Fri, 27 Jun 2003 09:13:18 UTC (12 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.DS
< prev   |   next >
new | recent | 2003-06

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

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

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

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.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)