Cesaro Limits for Fractional Dynamics
We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the asymptotic behavior of the random time dynamical systems. It t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/4/133 |
| _version_ | 1827672381510909952 |
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| author | Yuri Kondratiev José da Silva |
| author_facet | Yuri Kondratiev José da Silva |
| author_sort | Yuri Kondratiev |
| collection | DOAJ |
| description | We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the asymptotic behavior of the random time dynamical systems. It turns out that for the special case of stable subordinators explicit expressions for the subordination are known and its asymptotic behavior are derived. For more general classes of random time changes explicit calculations are essentially more complicated and we reduce our study to the asymptotic behavior of the corresponding Cesaro limit. |
| first_indexed | 2024-03-10T04:06:38Z |
| format | Article |
| id | doaj.art-c404466ae5a2485f9f55f15a82f16f13 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:06:38Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-c404466ae5a2485f9f55f15a82f16f132023-11-23T08:22:43ZengMDPI AGFractal and Fractional2504-31102021-09-015413310.3390/fractalfract5040133Cesaro Limits for Fractional DynamicsYuri Kondratiev0José da Silva1Department of Mathematics, University of Bielefeld, D-33615 Bielefeld, GermanyCIMA, University of Madeira, Campus da Penteada, 9020-105 Funchal, PortugalWe study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the asymptotic behavior of the random time dynamical systems. It turns out that for the special case of stable subordinators explicit expressions for the subordination are known and its asymptotic behavior are derived. For more general classes of random time changes explicit calculations are essentially more complicated and we reduce our study to the asymptotic behavior of the corresponding Cesaro limit.https://www.mdpi.com/2504-3110/5/4/133dynamical systemsrandom time changeinverse subordinatorasymptotic behavior |
| spellingShingle | Yuri Kondratiev José da Silva Cesaro Limits for Fractional Dynamics Fractal and Fractional dynamical systems random time change inverse subordinator asymptotic behavior |
| title | Cesaro Limits for Fractional Dynamics |
| title_full | Cesaro Limits for Fractional Dynamics |
| title_fullStr | Cesaro Limits for Fractional Dynamics |
| title_full_unstemmed | Cesaro Limits for Fractional Dynamics |
| title_short | Cesaro Limits for Fractional Dynamics |
| title_sort | cesaro limits for fractional dynamics |
| topic | dynamical systems random time change inverse subordinator asymptotic behavior |
| url | https://www.mdpi.com/2504-3110/5/4/133 |
| work_keys_str_mv | AT yurikondratiev cesarolimitsforfractionaldynamics AT josedasilva cesarolimitsforfractionaldynamics |