Journal of Nonlinear Mathematical Physics

Volume 21, Issue 1, February 2014, Pages 1 - 16

Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian

Authors
Sergi Simon
Department of Mathematics, University of Portsmouth Lion Gate Bldg, Lion Terrace Portsmouth PO1 3HF, UK. sergi.simon@port.ac.uk
Received 18 September 2013, Accepted 11 November 2013, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2014.894710How to use a DOI?
Keywords
Hamiltonian integrability, Differential Galois Theory, Ziglin-Morales-Ramis theory, Cosmology, Friedmann-Robertson-Walker metric, numerical detection of chaos, monodromy group
Abstract

This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Simó on higher-order variational equations, to the well-known Friedmann-Robertson-Walker cosmological model. A previous paper by the author formalises said variational systems in such a way allowing the simple expression of notable elements of the differential Galois group needed to study integrability. Using this formalisation and an alternative method already used by other authors, we find sufficient conditions whose fulfilment for given parameters would entail very simple proofs of non-integrability – both for the complete Hamiltonian, a goal already achieved by other means by Coelho et al, and for a special open case attracting recent attention.

Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 1
Pages
1 - 16
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2014.894710How to use a DOI?
Copyright
© 2014 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Sergi Simon
PY  - 2021
DA  - 2021/01
TI  - Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 16
VL  - 21
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.894710
DO  - https://doi.org/10.1080/14029251.2014.894710
ID  - Simon2021
ER  -