AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Communications in Analysis and Mechanics Article
PDF (326.8 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

An example in Hamiltonian dynamics

Institute of Mathematics, University of Warsaw, UL. Banacha 2, 02-097 Warsaw, Poland
Show Author Information

Abstract

We present an example of a three-degrees-of-freedom polynomial Hamilton function with a critical point characterized by indefinite quadratic part with a Morse index 2. This function generates a Hamiltonian system wherein all eigenvalues equal ±i, but it lacks small-amplitude periodic solutions with a period ≈2π.

Keywords

Hamiltonian systemperiodic solutionsLyapunov theorem
CLC number: Primary 05C38, 15A15; Secondary 05A15, 15A18

References

【1】
【1】
 
 
Crossref Google Scholar
Communications in Analysis and Mechanics
Volume 16 Issue 2,
June 2024
Pages 431-447
DOI: 10.3934/cam.2024020

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Żoła̧dek H. An example in Hamiltonian dynamics. Communications in Analysis and Mechanics, 2024, 16(2): 431-447. https://doi.org/10.3934/cam.2024020

458

Views

38

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 11 November 2023
Revised: 03 April 2024
Accepted: 08 May 2024
Published: 11 June 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)