Integrable cosmological potentials
Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient...
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| Autor*in: |
Sokolov, V. V. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Letters in mathematical physics - Springer Netherlands, 1975, 107(2017), 9 vom: 08. Mai, Seite 1741-1768 |
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| Übergeordnetes Werk: |
volume:107 ; year:2017 ; number:9 ; day:08 ; month:05 ; pages:1741-1768 |
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| DOI / URN: |
10.1007/s11005-017-0962-y |
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| 520 | |a Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. | ||
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10.1007/s11005-017-0962-y doi (DE-627)OLC2075490023 (DE-He213)s11005-017-0962-y-p DE-627 ger DE-627 rakwb eng 530 VZ Sokolov, V. V. verfasserin aut Integrable cosmological potentials 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. Liouville integrability Integrals of motion Nonlinear ODEs Sorin, A. S. aut Enthalten in Letters in mathematical physics Springer Netherlands, 1975 107(2017), 9 vom: 08. Mai, Seite 1741-1768 (DE-627)129436666 (DE-600)193974-9 (DE-576)014807467 0377-9017 nnns volume:107 year:2017 number:9 day:08 month:05 pages:1741-1768 https://doi.org/10.1007/s11005-017-0962-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4318 AR 107 2017 9 08 05 1741-1768 |
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10.1007/s11005-017-0962-y doi (DE-627)OLC2075490023 (DE-He213)s11005-017-0962-y-p DE-627 ger DE-627 rakwb eng 530 VZ Sokolov, V. V. verfasserin aut Integrable cosmological potentials 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. Liouville integrability Integrals of motion Nonlinear ODEs Sorin, A. S. aut Enthalten in Letters in mathematical physics Springer Netherlands, 1975 107(2017), 9 vom: 08. Mai, Seite 1741-1768 (DE-627)129436666 (DE-600)193974-9 (DE-576)014807467 0377-9017 nnns volume:107 year:2017 number:9 day:08 month:05 pages:1741-1768 https://doi.org/10.1007/s11005-017-0962-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4318 AR 107 2017 9 08 05 1741-1768 |
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10.1007/s11005-017-0962-y doi (DE-627)OLC2075490023 (DE-He213)s11005-017-0962-y-p DE-627 ger DE-627 rakwb eng 530 VZ Sokolov, V. V. verfasserin aut Integrable cosmological potentials 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. Liouville integrability Integrals of motion Nonlinear ODEs Sorin, A. S. aut Enthalten in Letters in mathematical physics Springer Netherlands, 1975 107(2017), 9 vom: 08. Mai, Seite 1741-1768 (DE-627)129436666 (DE-600)193974-9 (DE-576)014807467 0377-9017 nnns volume:107 year:2017 number:9 day:08 month:05 pages:1741-1768 https://doi.org/10.1007/s11005-017-0962-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4318 AR 107 2017 9 08 05 1741-1768 |
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10.1007/s11005-017-0962-y doi (DE-627)OLC2075490023 (DE-He213)s11005-017-0962-y-p DE-627 ger DE-627 rakwb eng 530 VZ Sokolov, V. V. verfasserin aut Integrable cosmological potentials 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. Liouville integrability Integrals of motion Nonlinear ODEs Sorin, A. S. aut Enthalten in Letters in mathematical physics Springer Netherlands, 1975 107(2017), 9 vom: 08. Mai, Seite 1741-1768 (DE-627)129436666 (DE-600)193974-9 (DE-576)014807467 0377-9017 nnns volume:107 year:2017 number:9 day:08 month:05 pages:1741-1768 https://doi.org/10.1007/s11005-017-0962-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4318 AR 107 2017 9 08 05 1741-1768 |
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10.1007/s11005-017-0962-y doi (DE-627)OLC2075490023 (DE-He213)s11005-017-0962-y-p DE-627 ger DE-627 rakwb eng 530 VZ Sokolov, V. V. verfasserin aut Integrable cosmological potentials 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2017 Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. Liouville integrability Integrals of motion Nonlinear ODEs Sorin, A. S. aut Enthalten in Letters in mathematical physics Springer Netherlands, 1975 107(2017), 9 vom: 08. Mai, Seite 1741-1768 (DE-627)129436666 (DE-600)193974-9 (DE-576)014807467 0377-9017 nnns volume:107 year:2017 number:9 day:08 month:05 pages:1741-1768 https://doi.org/10.1007/s11005-017-0962-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4310 GBV_ILN_4318 AR 107 2017 9 08 05 1741-1768 |
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Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. © Springer Science+Business Media Dordrecht 2017 |
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Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. © Springer Science+Business Media Dordrecht 2017 |
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Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed. © Springer Science+Business Media Dordrecht 2017 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2075490023</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503174158.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11005-017-0962-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2075490023</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11005-017-0962-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Sokolov, V. V.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integrable cosmological potentials</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media Dordrecht 2017</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field $$\varphi $$, which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint $$H=0$$, is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential $$V(\varphi )$$. In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. 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