  The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts
model are studied using the theory of dynamical systems. An exact recurrence
relation for the partition function is derived. It is shown that zeros of the
partition function may be associated with neutral fixed points of the
recurrence relation. Further, a general equation for zeros of the partition
function is found and a classification of the Yang-Lee, Fisher and Potts zeros
is given. It is shown that the Fisher zeros in a nonzero magnetic field are
located on several lines in the complex temperature plane and that the number
of these lines depends on the value of the magnetic field. Analytical
expressions for the densities of the Yang-Lee, Fisher and Potts zeros are
derived. It is shown that densities of all types of zeros of the partition
function are singular at the edge singularity points with the same critical
exponent \sigma=-1/2.
