%0 Journal Article %T On commuting Tonelli Hamiltonians: Time-periodic case %A Xiaojun Cui %J Mathematics %D 2010 %I arXiv %X We show that the Aubry sets, the Ma\~{n}\'{e} sets and Mather's barrier functions are the same for two commuting time-periodic Tonelli Hamiltonians. %U http://arxiv.org/abs/1001.1324v3