Abstract
The analysis of movable singularities in the complex time plane of n first order, ordinary differential equations has led to a better understanding of the real time behavior of the solutions of dynamical systems. The requirement that these singularities be poles, with n-1 free constants, i.e. the so-called Painlevé property, has identified many new completely integrable dynamical systems having, of course, no chaotic behavior whatsoever. On the other hand, the violation of the Painleve property with the introduction of logarithmic terms at higher orders in the series expansions has identified many dynamical systems with only "weakly chaotic" behavior. In this paper, I review these results and discuss the methods of singularity analysis with the aid of illustrative examples.
| Original language | English |
|---|---|
| Pages (from-to) | 353-373 |
| Number of pages | 21 |
| Journal | North-Holland Mathematics Studies |
| Volume | 103 |
| Issue number | C |
| DOIs | |
| Publication status | Published - 1985 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
A Singularity Analysis of Integrability and Chaos in Dynamical Systems. / Bountis, Tassos C.
In: North-Holland Mathematics Studies, Vol. 103, No. C, 1985, p. 353-373.Research output: Contribution to journal › Article
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TY - JOUR
T1 - A Singularity Analysis of Integrability and Chaos in Dynamical Systems
AU - Bountis, Tassos C.
PY - 1985
Y1 - 1985
N2 - The analysis of movable singularities in the complex time plane of n first order, ordinary differential equations has led to a better understanding of the real time behavior of the solutions of dynamical systems. The requirement that these singularities be poles, with n-1 free constants, i.e. the so-called Painlevé property, has identified many new completely integrable dynamical systems having, of course, no chaotic behavior whatsoever. On the other hand, the violation of the Painleve property with the introduction of logarithmic terms at higher orders in the series expansions has identified many dynamical systems with only "weakly chaotic" behavior. In this paper, I review these results and discuss the methods of singularity analysis with the aid of illustrative examples.
AB - The analysis of movable singularities in the complex time plane of n first order, ordinary differential equations has led to a better understanding of the real time behavior of the solutions of dynamical systems. The requirement that these singularities be poles, with n-1 free constants, i.e. the so-called Painlevé property, has identified many new completely integrable dynamical systems having, of course, no chaotic behavior whatsoever. On the other hand, the violation of the Painleve property with the introduction of logarithmic terms at higher orders in the series expansions has identified many dynamical systems with only "weakly chaotic" behavior. In this paper, I review these results and discuss the methods of singularity analysis with the aid of illustrative examples.
UR - http://www.scopus.com/inward/record.url?scp=77956934584&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956934584&partnerID=8YFLogxK
U2 - 10.1016/S0304-0208(08)72136-4
DO - 10.1016/S0304-0208(08)72136-4
M3 - Article
VL - 103
SP - 353
EP - 373
JO - North-Holland Mathematics Studies
JF - North-Holland Mathematics Studies
SN - 0304-0208
IS - C
ER -