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

DOI

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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TY  - JOUR
AU  - Sergi Simon
PY  - 2021
DA  - 2021/01/06
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  - 10.1080/14029251.2014.894710
ID  - Simon2021
ER  -