Abstract
The breakup of KAM tori in four-dimensional symplectic maps is studied. KAM tori are constructed explicitly by conjugation theory, and the successive steps leading to their breakup is analytically determined for two cases in which rotation vectors are cubic and quadratic. The present paper is motivated by the observation of Boltt and Meiss (Physica D66(1993), 282), but our result differs significantly from their conjecture, because it suggests that the rational approximation does not work in cases with many degrees of freedom. The succession to the breakup depends on the perturbations which determine the dominant type of small divisors in the conjugation function.
| Original language | English |
|---|---|
| Pages (from-to) | 783-793 |
| Number of pages | 11 |
| Journal | Progress of Theoretical Physics |
| Volume | 98 |
| Issue number | 4 |
| Publication status | Published - 1997 Oct |
Fingerprint
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Breakup process and geometrical structure of high-dimensional KAM tori. / Kurosaki, Satoru; Aizawa, Yoji.
In: Progress of Theoretical Physics, Vol. 98, No. 4, 10.1997, p. 783-793.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Breakup process and geometrical structure of high-dimensional KAM tori
AU - Kurosaki, Satoru
AU - Aizawa, Yoji
PY - 1997/10
Y1 - 1997/10
N2 - The breakup of KAM tori in four-dimensional symplectic maps is studied. KAM tori are constructed explicitly by conjugation theory, and the successive steps leading to their breakup is analytically determined for two cases in which rotation vectors are cubic and quadratic. The present paper is motivated by the observation of Boltt and Meiss (Physica D66(1993), 282), but our result differs significantly from their conjecture, because it suggests that the rational approximation does not work in cases with many degrees of freedom. The succession to the breakup depends on the perturbations which determine the dominant type of small divisors in the conjugation function.
AB - The breakup of KAM tori in four-dimensional symplectic maps is studied. KAM tori are constructed explicitly by conjugation theory, and the successive steps leading to their breakup is analytically determined for two cases in which rotation vectors are cubic and quadratic. The present paper is motivated by the observation of Boltt and Meiss (Physica D66(1993), 282), but our result differs significantly from their conjecture, because it suggests that the rational approximation does not work in cases with many degrees of freedom. The succession to the breakup depends on the perturbations which determine the dominant type of small divisors in the conjugation function.
UR - http://www.scopus.com/inward/record.url?scp=0031318666&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031318666&partnerID=8YFLogxK
M3 - Article
VL - 98
SP - 783
EP - 793
JO - Progress of Theoretical Physics
JF - Progress of Theoretical Physics
SN - 0033-068X
IS - 4
ER -