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

Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:1402.1102 (nlin)
[Submitted on 1 Feb 2014]

Title:Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system

Authors:V.Z. Enolski, Yu.N.Fedorov, A.N.W. Hone
View PDF
Abstract:It is known that the Jacobian of an algebraic curve which is a 2-fold covering of a hyperelliptic curve ramified at two points contains a hyperelliptic Prym variety. Its explicit algebraic description is applied to some of the integrable Henon-Heiles systems with a non-polynomial potential. Namely, we identify the generic complex invariant manifolds of the systems as a hyperelliptic Prym subvariety of the Jacobian of the spectral curve of the corresponding Lax representation.
The exact discretization of the system is described as a translation on the Prym variety.
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Algebraic Geometry (math.AG)
Cite as: arXiv:1402.1102 [nlin.SI]
  (or arXiv:1402.1102v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.1402.1102
Related DOI: https://doi.org/10.1016/j.geomphys.2014.01.004

Submission history

From: Andrew Hone N.W. [view email]
[v1] Sat, 1 Feb 2014 15:20:55 UTC (15 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
nlin.SI
< prev   |   next >
new | recent | 2014-02
Change to browse by:
math
math.AG
nlin

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?)