Bifurcations of beam-beam like maps

The bifurcations of a class of mappings including the beam-beam map are exa mined. These maps are asymptotically linear at infinity where they exhibit invariant curves and elliptic periodic points. The dynamical behaviour is r adically different with respect to the Henon-like polynomial maps whose sta bility 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 obse rves the disappearance of chains of islands born from the origin and coming from infinity. This behaviour has relevant consequences on the transport p rocess.