[en] The Dyson mapping is applied to the analysis of low-lying collective states in odd-mass nuclei. The original fermion (quasiparticle) space is truncated to a collective subspace which consists of products of collective phonons and a single fermion (quasiparticle). This subspace is mapped on an ideal boson-fermion space by the Dyson mapping and a simple but non-hermitian hamiltonian is obtained. The eigenvalue equations for the hamiltonian are numerically solved for the cases of the unique-parity states in the odd-mass Rh isotopes. The results show that the Dyson mapping is quite useful for analyses of phonon-particle coupling in odd-mass nuclei. (orig.)