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We investigate the Miura map between the dispersionless KP and dispersionlessmodified KP hierarchies. We show that the Miura map is canonical with respectto their bi-Hamiltonian structures. Moreover, inspired by the works of Takasakiand Takebe, the twistor construction of solution structure for thedispersionless modified KP hierarchy is given.Comment: 19 pages, Latex, no figure

On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies