Publication: Periodic solutions, KAM tori and bifurcations in a cosmology-inspired potential
| dc.contributor.author | Palacián Subiela, Jesús Francisco | |
| dc.contributor.author | Vidal Díaz, Claudio | |
| dc.contributor.author | Vidarte, Jhon | |
| dc.contributor.author | Yanguas Sayas, Patricia | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.date.accessioned | 2019-08-28T09:07:15Z | |
| dc.date.available | 2020-08-05T23:00:10Z | |
| dc.date.issued | 2019 | |
| dc.description | This is a peer-reviewed, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/ab1bc6. | en |
| dc.description.abstract | A family of perturbed Hamiltonians H = 1/2 (x^2 + X^2) − 1/2 (y^2 + Y^2)+1/2 (z^2 + Z^2) + 2[ (x^4 + y^4 + z^4) + (x^2 y^2 + x^2 z^2 + y^2 z^2)] in 1: −1:1 resonance depending on two real parameters is considered. We show the existence and stability of periodic solutions using reduction and averaging. In fact, there are at most thirteen families for every energy level h < 0 and at most twenty six families for every h > 0. The different types of periodic solutions for every nonzero energy level, as well as their bifurcations, are characterised in terms of the parameters. The linear stability of each family of periodic solutions, together with the determination of KAM 3-tori encasing some of the linearly stable periodic solutions is proved. Critical Hamiltonian bifurcations on the reduced space are characterised. We find important differences with respect to the dynamics of the 1:1:1 resonance with the same perturbation as the one given here. We end up with an intuitive interpretation of the results from a cosmological viewpoint. | en |
| dc.description.sponsorship | The authors are partially supported by Projects MTM 2011-28227-C02-01 of the Ministry of Science and Innovation of Spain, MTM 2014-59433-C2-1-P of the Ministry of Economy and Competitiveness of Spain and MTM 2017-88137-C2-1-P of the Ministry of Science, Innovation and Universities of Spain. C Vidal is partially supported by Project Fondecyt 1180288. | en |
| dc.embargo.lift | 2020-08-05 | |
| dc.embargo.terms | 2020-08-05 | |
| dc.format.extent | 37 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1088/1361-6544/ab1bc6 | |
| dc.identifier.issn | 0951-7715 (Print) | |
| dc.identifier.issn | 1361-6544 (Electronic) | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/34657 | |
| dc.language.iso | eng | en |
| dc.publisher | IOP Publishing | en |
| dc.relation.ispartof | Nonlinearity 32 3406 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-28227-C02-01/ES/ | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-59433-C2-1-P/ES/ | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88137-C2-1-P/ES/ | en |
| dc.relation.publisherversion | https://doi.org/10.1088/1361-6544/ab1bc6 | |
| dc.rights | © 2019 IOP Publishing Ltd & London Mathematical Society | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Resonant Hamiltonians | en |
| dc.subject | Friedmann–Lemaître–Robertson–Walker model | en |
| dc.subject | Normalisation and reduction | en |
| dc.subject | Hamiltonian Hopf bifurcation | en |
| dc.subject | KAM tori | en |
| dc.subject | Cosmological Hamiltonian | en |
| dc.subject | Reduced space and invariants | en |
| dc.title | Periodic solutions, KAM tori and bifurcations in a cosmology-inspired potential | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
| dspace.entity.type | Publication | |
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