RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2018, Volume 23, Issue 3, Pages 248–256 (Mi rcd321)  

The Spectrum of Reversible Minimizers

Antonio J. Ureña

Departamento de Matematica Aplicada, Facultad de Ciencias, Universidad de Granada, Granada, 18071 Spain

Abstract: Poincaré and, later on, Carathéodory, showed that the Floquet multipliers of 1-dimensional periodic curves minimizing the Lagrangian action are real and positive. Even though Carathéodory himself observed that this result loses its validity in the general higherdimensional case, we shall show that it remains true for systems which are reversible in time. In this way, we also generalize a previous result by Offin on the hyperbolicity of nondegenerate symmetric minimizers. Our arguments rely on the higher-dimensional generalizations of the Sturm theory which were developed during the second half of the twentieth century by several authors, including Hartman, Morse or Arnol’d.

Keywords: action minimizers, Floquet multipliers, time reversibility

Funding Agency Grant Number
Federación Española de Enfermedades Raras MTM2014- 5223
The author is partially supported by Spanish MICINN Grant with FEDER funds MTM2014-5223.


DOI: https://doi.org/10.1134/S1560354718030024

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J25, 37J50, 34D08
Received: 17.10.2017
Accepted:17.02.2018
Language:

Citation: Antonio J. Ureña, “The Spectrum of Reversible Minimizers”, Regul. Chaotic Dyn., 23:3 (2018), 248–256

Citation in format AMSBIB
\Bibitem{Ure18}
\by Antonio J. Ure\~na
\paper The Spectrum of Reversible Minimizers
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 3
\pages 248--256
\mathnet{http://mi.mathnet.ru/rcd321}
\crossref{https://doi.org/10.1134/S1560354718030024}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3811817}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018RCD....23..248U}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000434637700002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048122616}


Linking options:
  • http://mi.mathnet.ru/eng/rcd321
  • http://mi.mathnet.ru/eng/rcd/v23/i3/p248

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:35
    References:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020