Asymptotic effects in jet production at high energies

Monte Carlo event simulation with BFKL evolution is discussed. We report current status of a Monte Carlo event generator ULYSSES with BFKL evolution implemented. The ULYSSES, based on Pythia Monte Carlo generator, would help to reveal BFKL effects at LHC energies. In particular, such an observable as dijet K-factor can serve as a source of BFKL dynamics at the LHC, and it would also help to search for new physics.