  The R\"ossler System is one of the best known chaotic dynamical systems,
exhibiting a plethora of complex phenomena - and yet, only a few studies
tackled its complexity analytically. Building on previous work by the author,
in this paper we characterize the dynamical complexity for the R\"ossler System
at parameter values at which the flow satisfies a certain heteroclinic
condition. This will allow us to characterize the knot type of infinitely many
periodic trajectories for the flow - and reduce the R\"ossler system to a
simpler hyperbolic flow, capturing its essential dynamics.
