A path integral equation formalism is developed to obtain the frequency spectrum of nonlinear mappings exhibiting chaotic behavior. The one‐dimensional map,xn+1=f(xn), wherefis nonlinear andnis a discrete time variable, is analyzed in detail. This map is introduced as a paradigm of systems whose exact behavior is exceedingly complex, and therefore irretrievable, but which nevertheless possess smooth, well‐behaved solutions in the presence of small sources of external noise. A Boltzmann integral equation is derived for the probability distriburtion functionp(x,n). This equation is linear and is therefore amenable to spectral analysis. The nonlinear dynamics inf(x) appear as transition probability matrix elements, and the presence of noise appears simply as an overall multiplicative scattering amplitude. This formalism is used to investigate the band structure of the logistic equation and to analyze the effects of external noise on both the invariant measure and the frequency spectrum ofxnfor several values of &lgr;∈[0,1].