TY - JOUR
TI - Bifurcations of beam-beam like maps
AU - Polymilis, C
AU - Skokos, C
AU - Kollias, G
AU - Servizi, G
AU - Turchetti,
AU - G
JO - Journal of Physics A: Mathematical and General
PY - 2000
VL - 33
TODO - 5
SP - 1055-1064
PB - IOP Publishing Ltd
SN - 0305-4470, 1361-6447
TODO - 10.1088/0305-4470/33/5/316
TODO - null
TODO - The bifurcations of a class of mappings including the beam-beam map are
examined. These maps are asymptotically linear at infinity where they
exhibit invariant curves and elliptic periodic points. The dynamical
behaviour is radically different with respect to the Henon-like
polynomial maps whose stability boundary (dynamic aperture) is at a
finite distance. Rather than the period-doubling bifurcations exhibited
by the Henon-like maps, we observe a systematic appearance of tangent
bifurcations and in phase space one observes the disappearance of chains
of islands born from the origin and coming from infinity. This behaviour
has relevant consequences on the transport process.
ER -