Abstract
In the extended standard map, the critical line for breakup of an invariant circle contains, for almost all rotation numbers, a Cantor set of cusps in parameter space. The Farey route to a given rotation number illustrates how the cusps appear and allows the characterization of their pattern. The fact that the cusp-splitting rules seem attainable by the Farey route rather than by the convergents must be incorporated in the renormalization theory.
| Original language | English |
|---|---|
| Pages (from-to) | 775-780 |
| Number of pages | 6 |
| Journal | Physical Review A |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Jan 1990 |
| MoE publication type | Not Eligible |
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Breakup of Kolmogorov-Arnold-Moser tori of arbitrary frequency in a two-parameter system. / Ketoja, Jukka A.
In: Physical Review A, Vol. 42, No. 2, 01.01.1990, p. 775-780.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Breakup of Kolmogorov-Arnold-Moser tori of arbitrary frequency in a two-parameter system
AU - Ketoja, Jukka A.
PY - 1990/1/1
Y1 - 1990/1/1
N2 - In the extended standard map, the critical line for breakup of an invariant circle contains, for almost all rotation numbers, a Cantor set of cusps in parameter space. The Farey route to a given rotation number illustrates how the cusps appear and allows the characterization of their pattern. The fact that the cusp-splitting rules seem attainable by the Farey route rather than by the convergents must be incorporated in the renormalization theory.
AB - In the extended standard map, the critical line for breakup of an invariant circle contains, for almost all rotation numbers, a Cantor set of cusps in parameter space. The Farey route to a given rotation number illustrates how the cusps appear and allows the characterization of their pattern. The fact that the cusp-splitting rules seem attainable by the Farey route rather than by the convergents must be incorporated in the renormalization theory.
UR - http://www.scopus.com/inward/record.url?scp=4243209366&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.42.775
DO - 10.1103/PhysRevA.42.775
M3 - Article
AN - SCOPUS:4243209366
VL - 42
SP - 775
EP - 780
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 2
ER -