American companies hailing from sea to shining sea are presented here by the Joyce Theater and White Bird, an influential Portland, Ore., dance organization, as part of the tsunami of dance showcases hitting New York for the annual gathering of arts presenters. The four split-bill programs will pair established troupes, like the Martha Graham Dance Company, Hubbard Street Dance Chicago and Alonzo King's Lines Ballet, with young collectives that are generating buzz, like TU Dance out of St. Paul and Ate9 from Los Angeles.