Discrete-Time Goldfishing
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several o...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147409 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
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Calogero, F. 2019-02-14T17:53:55Z 2019-02-14T17:53:55Z 2011 Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 37C27; 70F10; 70H06 DOI: http://dx.doi.org/10.3842/SIGMA.2011.082 https://nasplib.isofts.kiev.ua/handle/123456789/147409 The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞. This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html. It is a pleasure to thank my colleague and friend Orlando Ragnisco for pointing out relevant references. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Discrete-Time Goldfishing Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Discrete-Time Goldfishing |
| spellingShingle |
Discrete-Time Goldfishing Calogero, F. |
| title_short |
Discrete-Time Goldfishing |
| title_full |
Discrete-Time Goldfishing |
| title_fullStr |
Discrete-Time Goldfishing |
| title_full_unstemmed |
Discrete-Time Goldfishing |
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discrete-time goldfishing |
| author |
Calogero, F. |
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Calogero, F. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
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Article |
| description |
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147409 |
| citation_txt |
Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
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