AbstractThe ranges of the transfer and the return maps that are induced by the flow of a piecewise‐linear continuous dynamical system describing Chua's circuit are investigated analytically. the two sets turn out to be intertwined for all values of the parameters. For high enough frequencies of the saddle‐focus, located at the origin of state space, the first set forms ‘inclusions’ inside the second one. A charting of parameter space describing the creation and annihilation of the above inclusions quantitatively is in