Abstract
Infinite sequences of period-doubling bifurcations are known to occur generically (i.e. with codimension 1) not only in dissipative 1D systems but also in 2D conservative systems, described by area-preserving mappings. In this paper, we study a 3D volume-preserving, reversible mapping and show that it does possess period 2m(m=1,2,...) orbits, with stability intervals whose length decreases rapidly, with increasing m. Varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period-doubling sequences of 2D-conservative maps. This raises the interesting question whether these 3D reversible maps possess an analytic integral which would render them essentially 2-dimensional.
| Original language | English |
|---|---|
| Pages (from-to) | 218-233 |
| Number of pages | 16 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 211 |
| Issue number | 2-3 |
| DOIs | |
| Publication status | Published - Nov 1 1994 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
2D universality of period-doubling bifurcations in 3D conservative reversible mappings. / Komineas, Stavros; Vrahatis, Michael N.; Bountis, Tassos.
In: Physica A: Statistical Mechanics and its Applications, Vol. 211, No. 2-3, 01.11.1994, p. 218-233.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - 2D universality of period-doubling bifurcations in 3D conservative reversible mappings
AU - Komineas, Stavros
AU - Vrahatis, Michael N.
AU - Bountis, Tassos
PY - 1994/11/1
Y1 - 1994/11/1
N2 - Infinite sequences of period-doubling bifurcations are known to occur generically (i.e. with codimension 1) not only in dissipative 1D systems but also in 2D conservative systems, described by area-preserving mappings. In this paper, we study a 3D volume-preserving, reversible mapping and show that it does possess period 2m(m=1,2,...) orbits, with stability intervals whose length decreases rapidly, with increasing m. Varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period-doubling sequences of 2D-conservative maps. This raises the interesting question whether these 3D reversible maps possess an analytic integral which would render them essentially 2-dimensional.
AB - Infinite sequences of period-doubling bifurcations are known to occur generically (i.e. with codimension 1) not only in dissipative 1D systems but also in 2D conservative systems, described by area-preserving mappings. In this paper, we study a 3D volume-preserving, reversible mapping and show that it does possess period 2m(m=1,2,...) orbits, with stability intervals whose length decreases rapidly, with increasing m. Varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period-doubling sequences of 2D-conservative maps. This raises the interesting question whether these 3D reversible maps possess an analytic integral which would render them essentially 2-dimensional.
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U2 - 10.1016/0378-4371(94)00040-9
DO - 10.1016/0378-4371(94)00040-9
M3 - Article
AN - SCOPUS:43949157592
VL - 211
SP - 218
EP - 233
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 2-3
ER -